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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sinx
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Integral of cosx^2
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Integral of sinh(x)
- Integral of xcos(nx)
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Identical expressions
- one /(x³+ one)
- 1 divide by (x³ plus 1)
- one divide by (x³ plus one)
- 1/x³+1
- 1 divide by (x³+1)
- 1/(x³+1)dx
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Similar expressions
- 1/(x³-1)
- 1/((x³+1))
Integral of 1/(x³+1) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 3 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} + 1}\, dx$$
Integral(1/(x^3 + 1), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ \ / ___ |2*\/ 3 *(-1/2 + x)| | / 2 \ \/ 3 *atan|------------------| | 1 log\1 + x - x/ log(1 + x) \ 3 / | ------ dx = C - --------------- + ---------- + ------------------------------ | 3 6 3 3 | x + 1 | /
$$\int \frac{1}{x^{3} + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer
[src]
___ log(2) pi*\/ 3 ------ + -------- 3 9
$$\frac{\log{\left(2 \right)}}{3} + \frac{\sqrt{3} \pi}{9}$$
=
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___ log(2) pi*\/ 3 ------ + -------- 3 9
$$\frac{\log{\left(2 \right)}}{3} + \frac{\sqrt{3} \pi}{9}$$
log(2)/3 + pi*sqrt(3)/9
The graph
Use the examples entering the upper and lower limits of integration.