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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^4/(1-x^2)
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Integral of 6/x^2
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Integral of √(x+4)
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Integral of sin(2x)cos(2x)
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Identical expressions
- one /(x³- one)
- 1 divide by (x³ minus 1)
- one divide by (x³ minus one)
- 1/x³-1
- 1 divide by (x³-1)
- 1/(x³-1)dx
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Similar expressions
- 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]
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
=
=
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
-oo - pi*i/3
The graph
Use the examples entering the upper and lower limits of integration.