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How to use it?
- Integral of d{x}:
- Integral of |x-1|
- Integral of sqrt(1+e^(2x))
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Integral of 2cos2x
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Integral of 1/4
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Identical expressions
- one /(one +x^(2n))
- 1 divide by (1 plus x to the power of (2n))
- one divide by (one plus x to the power of (2n))
- 1/(1+x(2n))
- 1/1+x2n
- 1/1+x^2n
- 1 divide by (1+x^(2n))
- 1/(1+x^(2n))dx
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Similar expressions
- 1/(1-x^(2n))
Integral of 1/(1+x^(2n)) dx
The solution
You have entered
[src]
1 / | | 1 | -------- dx | 2*n | 1 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{2 n} + 1}\, dx$$
Integral(1/(1 + x^(2*n)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / 1 \ / 2*n pi*I 1 \ | x*Gamma|---|*lerchphi|x *e , 1, ---| | 1 \2*n/ \ 2*n/ | -------- dx = C + ----------------------------------------- | 2*n 2 / 1 \ | 1 + x 4*n *Gamma|1 + ---| | \ 2*n/ /
$$\int \frac{1}{x^{2 n} + 1}\, dx = C + \frac{x \Phi\left(x^{2 n} e^{i \pi}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)}$$
The answer
[src]
/ 1 \ / pi*I 1 \
Gamma|---|*lerchphi|e , 1, ---|
\2*n/ \ 2*n/
----------------------------------
2 / 1 \
4*n *Gamma|1 + ---|
\ 2*n/
$$\frac{\Phi\left(e^{i \pi}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)}$$
=
=
/ 1 \ / pi*I 1 \
Gamma|---|*lerchphi|e , 1, ---|
\2*n/ \ 2*n/
----------------------------------
2 / 1 \
4*n *Gamma|1 + ---|
\ 2*n/
$$\frac{\Phi\left(e^{i \pi}, 1, \frac{1}{2 n}\right) \Gamma\left(\frac{1}{2 n}\right)}{4 n^{2} \Gamma\left(1 + \frac{1}{2 n}\right)}$$
gamma(1/(2*n))*lerchphi(exp_polar(pi*i), 1, 1/(2*n))/(4*n^2*gamma(1 + 1/(2*n)))
Use the examples entering the upper and lower limits of integration.