Mixing
$int^infty_0 frac{dx}{x^n + 1}$, n odd [duplicate]
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This question already has an answer here:
Closed form for $ int_0^infty {frac{{{x^n}}}{{1 + {x^m}}}dx }$
10 answers
$int_{0}^{infty} frac{1}{1 + x^r}:dx = frac{1}{r}Gammaleft( frac{r - 1}{r}right)Gammaleft( frac{1}{r}right)$ [duplicate]
3 answers
Well, I saw this integral :
$$int^infty_0 frac{dx}{x^n + 1}$$
on some questions (like this one : Calculating a real integral using complex integration )
But it has always been for $n$ even.
Is there something wrong with $n$ odd ? Is not, how do you compute this ? by the same argument ?
thank you and sorry if this is easy. I can't figure out how to do it since it's neither odd nor even.
integration complex-analysis definite-integrals improper-integrals
edited Jan 7 at 11:06
Harry Peter
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
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marked as duplicate by mrtaurho, Zacky, Community♦ Jan 1 at 16:11
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Closed form for $ int_0^infty {frac{{{x^n}}}{{1 + {x^m}}}dx }$
10 answers
$int_{0}^{infty} frac{1}{1 + x^r}:dx = frac{1}{r}Gammaleft( frac{r - 1}{r}right)Gammaleft( frac{1}{r}right)$ [duplicate]
3 answers
Well, I saw this integral :
$$int^infty_0 frac{dx}{x^n + 1}$$
on some questions (like this one : Calculating a real integral using complex integration )
But it has always been for $n$ even.
Is there something wrong with $n$ odd ? Is not, how do you compute this ? by the same argument ?
thank you and sorry if this is easy. I can't figure out how to do it since it's neither odd nor even.
integration complex-analysis definite-integrals improper-integrals
edited Jan 7 at 11:06
Harry Peter
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
$endgroup$
marked as duplicate by mrtaurho, Zacky, Community♦ Jan 1 at 16:11
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
2
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46
add a comment |
$begingroup$
This question already has an answer here:
Closed form for $ int_0^infty {frac{{{x^n}}}{{1 + {x^m}}}dx }$
10 answers
$int_{0}^{infty} frac{1}{1 + x^r}:dx = frac{1}{r}Gammaleft( frac{r - 1}{r}right)Gammaleft( frac{1}{r}right)$ [duplicate]
3 answers
Well, I saw this integral :
$$int^infty_0 frac{dx}{x^n + 1}$$
on some questions (like this one : Calculating a real integral using complex integration )
But it has always been for $n$ even.
Is there something wrong with $n$ odd ? Is not, how do you compute this ? by the same argument ?
thank you and sorry if this is easy. I can't figure out how to do it since it's neither odd nor even.
integration complex-analysis definite-integrals improper-integrals
edited Jan 7 at 11:06
Harry Peter
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
$endgroup$
This question already has an answer here:
Closed form for $ int_0^infty {frac{{{x^n}}}{{1 + {x^m}}}dx }$
10 answers
$int_{0}^{infty} frac{1}{1 + x^r}:dx = frac{1}{r}Gammaleft( frac{r - 1}{r}right)Gammaleft( frac{1}{r}right)$ [duplicate]
3 answers
Well, I saw this integral :
$$int^infty_0 frac{dx}{x^n + 1}$$
on some questions (like this one : Calculating a real integral using complex integration )
But it has always been for $n$ even.
Is there something wrong with $n$ odd ? Is not, how do you compute this ? by the same argument ?
thank you and sorry if this is easy. I can't figure out how to do it since it's neither odd nor even.
This question already has an answer here:
Closed form for $ int_0^infty {frac{{{x^n}}}{{1 + {x^m}}}dx }$
10 answers
$int_{0}^{infty} frac{1}{1 + x^r}:dx = frac{1}{r}Gammaleft( frac{r - 1}{r}right)Gammaleft( frac{1}{r}right)$ [duplicate]
3 answers
integration complex-analysis definite-integrals improper-integrals
integration complex-analysis definite-integrals improper-integrals
edited Jan 7 at 11:06
Harry Peter
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
edited Jan 7 at 11:06
Harry Peter
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
edited Jan 7 at 11:06
Harry Peter
5,47111439
edited Jan 7 at 11:06
Harry Peter
5,47111439
edited Jan 7 at 11:06
Harry Peter
5,47111439
5,47111439
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
asked Jan 1 at 15:32
Marine GalantinMarine Galantin
700215
700215
marked as duplicate by mrtaurho, Zacky, Community♦ Jan 1 at 16:11
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by mrtaurho, Zacky, Community♦ Jan 1 at 16:11
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
2
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46
add a comment |
$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
2
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46
$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
2
2
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46
add a comment |
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$begingroup$
Integrate over a sector of a circle centred at the origin, with one side on the $x$-axis, and the other side making an angle of $2pi/n$ with it.
$endgroup$
– Lord Shark the Unknown
Jan 1 at 15:36
2
$begingroup$
Hi! You can also just set $n=0$ here: math.stackexchange.com/q/110457/515527 and obtain what you desire.
$endgroup$
– Zacky
Jan 1 at 15:38
$begingroup$
Thank you I ll check that. I think it solves my problem.
$endgroup$
– Marine Galantin
Jan 1 at 15:46