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How to use it?
- Integral of d{x}:
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Integral of cot^5xdx
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Integral of 1/(sqrt(x))
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Integral of (1-2*x)*exp(-2*x)
- Integral of (x^n)/(x+1)
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Identical expressions
- (x^n)/(x+ one)
- (x to the power of n) divide by (x plus 1)
- (x to the power of n) divide by (x plus one)
- (xn)/(x+1)
- xn/x+1
- x^n/x+1
- (x^n) divide by (x+1)
- (x^n)/(x+1)dx
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Similar expressions
- (x^n)/(x-1)
Integral of (x^n)/(x+1) dx
The solution
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[src]
1 / | | n | x | ----- dx | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x^{n}}{x + 1}\, dx$$
Integral(x^n/(x + 1), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | n n / pi*I \ n / pi*I \ | x x*x *Gamma(1 + n)*lerchphi\x*e , 1, 1 + n/ n*x*x *Gamma(1 + n)*lerchphi\x*e , 1, 1 + n/ | ----- dx = C + --------------------------------------------- + ----------------------------------------------- | x + 1 Gamma(2 + n) Gamma(2 + n) | /
$$\int \frac{x^{n}}{x + 1}\, dx = C + \frac{n x x^{n} \Phi\left(x e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{x x^{n} \Phi\left(x e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
The answer
[src]
/ pi*I \ / pi*I \
Gamma(1 + n)*lerchphi\e , 1, 1 + n/ n*Gamma(1 + n)*lerchphi\e , 1, 1 + n/
-------------------------------------- + ----------------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
=
=
/ pi*I \ / pi*I \
Gamma(1 + n)*lerchphi\e , 1, 1 + n/ n*Gamma(1 + n)*lerchphi\e , 1, 1 + n/
-------------------------------------- + ----------------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Phi\left(e^{i \pi}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)}$$
gamma(1 + n)*lerchphi(exp_polar(pi*i), 1, 1 + n)/gamma(2 + n) + n*gamma(1 + n)*lerchphi(exp_polar(pi*i), 1, 1 + n)/gamma(2 + n)
Use the examples entering the upper and lower limits of integration.