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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x*2^x
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Integral of x*sin(x/2)
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Integral of x^4/(x^2+1)
- Integral of x^2*a^x
- Derivative of:
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(x^2+1)/(x^3-1)
- Graphing y =:
- (x^2+1)/(x^3-1)
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Identical expressions
- (x^ two + one)/(x^ three - one)
- (x squared plus 1) divide by (x cubed minus 1)
- (x to the power of two plus one) divide by (x to the power of three minus one)
- (x2+1)/(x3-1)
- x2+1/x3-1
- (x²+1)/(x³-1)
- (x to the power of 2+1)/(x to the power of 3-1)
- x^2+1/x^3-1
- (x^2+1) divide by (x^3-1)
- (x^2+1)/(x^3-1)dx
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Similar expressions
- (x^2-1)/(x^3-1)
- (x^2+1)/(x^3+1)
Integral of (x^2+1)/(x^3-1) dx
The solution
You have entered
[src]
1 / | | 2 | x + 1 | ------ dx | 3 | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{x^{2} + 1}{x^{3} - 1}\, dx$$
Integral((x^2 + 1)/(x^3 - 1), (x, 0, 1))
The answer (Indefinite)
[src]
/ / ___ \ | ___ |2*\/ 3 *(1/2 + x)| | 2 / 2\ \/ 3 *atan|-----------------| | x + 1 log\1 + x + x / 2*log(-1 + x) \ 3 / | ------ dx = C + --------------- + ------------- - ----------------------------- | 3 6 3 3 | x - 1 | /
$$\int \frac{x^{2} + 1}{x^{3} - 1}\, dx = C + \frac{2 \log{\left(x - 1 \right)}}{3} + \frac{\log{\left(x^{2} + x + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer
[src]
2*pi*I
-oo - ------
3
$$-\infty - \frac{2 i \pi}{3}$$
=
=
2*pi*I
-oo - ------
3
$$-\infty - \frac{2 i \pi}{3}$$
-oo - 2*pi*i/3
The graph
Use the examples entering the upper and lower limits of integration.