$int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\$ [on hold]
Could I please have some starting points on solving the following indefinite integral:
$$int frac{1 - sin(x)}{1+sin(x)} space dx\$$
Is there a known method(s) for tackling this sort of integral?
integration indefinite-integrals trigonometric-integrals
edited Jan 8 at 0:01
DavidG
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asked Jan 6 at 17:54
Neil WernerNeil Werner
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Could I please have some starting points on solving the following indefinite integral:
$$int frac{1 - sin(x)}{1+sin(x)} space dx\$$
Is there a known method(s) for tackling this sort of integral?
integration indefinite-integrals trigonometric-integrals
edited Jan 8 at 0:01
DavidG
1,951620
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark Jan 6 at 19:32
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Could I please have some starting points on solving the following indefinite integral:
$$int frac{1 - sin(x)}{1+sin(x)} space dx\$$
Is there a known method(s) for tackling this sort of integral?
integration indefinite-integrals trigonometric-integrals
edited Jan 8 at 0:01
DavidG
1,951620
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Could I please have some starting points on solving the following indefinite integral:
$$int frac{1 - sin(x)}{1+sin(x)} space dx\$$
Is there a known method(s) for tackling this sort of integral?
integration indefinite-integrals trigonometric-integrals
integration indefinite-integrals trigonometric-integrals
edited Jan 8 at 0:01
DavidG
1,951620
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 8 at 0:01
DavidG
1,951620
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
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Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Jan 8 at 0:01
DavidG
1,951620
edited Jan 8 at 0:01
DavidG
1,951620
edited Jan 8 at 0:01
DavidG
1,951620
1,951620
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Jan 6 at 17:54
Neil WernerNeil Werner
153
asked Jan 6 at 17:54
Neil WernerNeil Werner
153
153
New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Neil Werner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark Jan 6 at 19:32
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark Jan 6 at 19:32
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, RRL, Lord Shark the Unknown, Holo, Hans Lundmark
If this question can be reworded to fit the rules in the help center, please edit the question.
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1 Answer
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Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$
edited Jan 6 at 18:22
Shubham Johri
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
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Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$
edited Jan 6 at 18:22
Shubham Johri
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$
edited Jan 6 at 18:22
Shubham Johri
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$
edited Jan 6 at 18:22
Shubham Johri
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$
edited Jan 6 at 18:22
Shubham Johri
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 6 at 18:22
Shubham Johri
4,651717
edited Jan 6 at 18:22
Shubham Johri
4,651717
edited Jan 6 at 18:22
Shubham Johri
4,651717
4,651717
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
answered Jan 6 at 17:59
Maximilian JanischMaximilian Janisch
46110
46110
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Maximilian Janisch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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