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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^(2*x)*cos(3*x)
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Integral of (2x-4)
- Integral of (3-sin(x))/(2cos(x)+3tan(x))
- Integral of (x)/(x^3-1)
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Identical expressions
- (x)/(x^ three - one)
- (x) divide by (x cubed minus 1)
- (x) divide by (x to the power of three minus one)
- (x)/(x3-1)
- x/x3-1
- (x)/(x³-1)
- (x)/(x to the power of 3-1)
- x/x^3-1
- (x) divide by (x^3-1)
- (x)/(x^3-1)dx
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Similar expressions
- x/(x^3-1)
- (x)/(x^3+1)
- x/(x^3)-1
- x/((x^3)-1)
Integral of (x)/(x^3-1) dx
The solution
You have entered
[src]
1 / | | x | ------ dx | 3 | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x}{x^{3} - 1}\, dx$$
Integral(x/(x^3 - 1*1), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ \ / ___ |2*\/ 3 *(1/2 + x)| | / 2\ \/ 3 *atan|-----------------| | x log\1 + x + x / log(-1 + x) \ 3 / | ------ dx = C - --------------- + ----------- + ----------------------------- | 3 6 3 3 | x - 1 | /
$$\int \frac{x}{x^{3} - 1}\, dx = C + \frac{\log{\left(x - 1 \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}}{3}$$
The answer
[src]
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
=
=
pi*I
-oo - ----
3
$$-\infty - \frac{i \pi}{3}$$
Use the examples entering the upper and lower limits of integration.