Finding the value of integral.
If $ int_{-infty}^{infty} f(x) dx= 1,$
Find value of $ int_{-infty}^{infty} f(x-frac{1}{x}) dx$.
I tried substituting $x$ as $frac{1}{t}$, but nothing is happening.
In the denominator, $1+x^2$ is left.
definite-integrals
edited 2 days ago
Gnumbertester
1285
asked 2 days ago
Math_centricMath_centric
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If $ int_{-infty}^{infty} f(x) dx= 1,$
Find value of $ int_{-infty}^{infty} f(x-frac{1}{x}) dx$.
I tried substituting $x$ as $frac{1}{t}$, but nothing is happening.
In the denominator, $1+x^2$ is left.
definite-integrals
edited 2 days ago
Gnumbertester
1285
asked 2 days ago
Math_centricMath_centric
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Hint: Try substituting $x=e^u$.
– John Doe
2 days ago
add a comment |
If $ int_{-infty}^{infty} f(x) dx= 1,$
Find value of $ int_{-infty}^{infty} f(x-frac{1}{x}) dx$.
I tried substituting $x$ as $frac{1}{t}$, but nothing is happening.
In the denominator, $1+x^2$ is left.
definite-integrals
edited 2 days ago
Gnumbertester
1285
asked 2 days ago
Math_centricMath_centric
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
If $ int_{-infty}^{infty} f(x) dx= 1,$
Find value of $ int_{-infty}^{infty} f(x-frac{1}{x}) dx$.
I tried substituting $x$ as $frac{1}{t}$, but nothing is happening.
In the denominator, $1+x^2$ is left.
definite-integrals
definite-integrals
edited 2 days ago
Gnumbertester
1285
asked 2 days ago
Math_centricMath_centric
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Gnumbertester
1285
asked 2 days ago
Math_centricMath_centric
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Gnumbertester
1285
edited 2 days ago
Gnumbertester
1285
edited 2 days ago
Gnumbertester
1285
1285
asked 2 days ago
Math_centricMath_centric
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Math_centricMath_centric
111
asked 2 days ago
Math_centricMath_centric
111
111
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Math_centric is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Hint: Try substituting $x=e^u$.
– John Doe
2 days ago
add a comment |
Hint: Try substituting $x=e^u$.
– John Doe
2 days ago
Hint: Try substituting $x=e^u$.
– John Doe
2 days ago
Hint: Try substituting $x=e^u$.
– John Doe
2 days ago
add a comment |
1 Answer
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One may recall the following property
$$
int_{-infty}^{+infty} f(x) , dx = int_{-infty}^{+infty} fleft( x - frac{1}{x} right) , dx
$$ proved here.
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
One may recall the following property
$$
int_{-infty}^{+infty} f(x) , dx = int_{-infty}^{+infty} fleft( x - frac{1}{x} right) , dx
$$ proved here.
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
add a comment |
One may recall the following property
$$
int_{-infty}^{+infty} f(x) , dx = int_{-infty}^{+infty} fleft( x - frac{1}{x} right) , dx
$$ proved here.
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
add a comment |
One may recall the following property
$$
int_{-infty}^{+infty} f(x) , dx = int_{-infty}^{+infty} fleft( x - frac{1}{x} right) , dx
$$ proved here.
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
One may recall the following property
$$
int_{-infty}^{+infty} f(x) , dx = int_{-infty}^{+infty} fleft( x - frac{1}{x} right) , dx
$$ proved here.
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
answered 2 days ago
Olivier OloaOlivier Oloa
108k17176293
108k17176293
add a comment |
add a comment |
Math_centric is a new contributor. Be nice, and check out our Code of Conduct.
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Hint: Try substituting $x=e^u$.
– John Doe
2 days ago