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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sin(5x)
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Integral of x/(x^3+8)
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Integral of x*e^(5*x)*dx
- Integral of 1/(x+lnx)
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Identical expressions
- x/(x^ three + eight)
- x divide by (x cubed plus 8)
- x divide by (x to the power of three plus eight)
- x/(x3+8)
- x/x3+8
- x/(x³+8)
- x/(x to the power of 3+8)
- x/x^3+8
- x divide by (x^3+8)
- x/(x^3+8)dx
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Similar expressions
- x/(x^3-8)
Integral of x/(x^3+8) dx
The solution
You have entered
[src]
oo / | | x | ------ dx | 3 | x + 8 | / 0
$$\int\limits_{0}^{\infty} \frac{x}{x^{3} + 8}\, dx$$
Integral(x/(x^3 + 8), (x, 0, oo))
The answer (Indefinite)
[src]
/ ___ \ / ___ |\/ 3 *(-1 + x)| | / 2 \ \/ 3 *atan|--------------| | x log(2 + x) log\4 + x - 2*x/ \ 3 / | ------ dx = C - ---------- + ----------------- + -------------------------- | 3 6 12 6 | x + 8 | /
$$\int \frac{x}{x^{3} + 8}\, dx = C - \frac{\log{\left(x + 2 \right)}}{6} + \frac{\log{\left(x^{2} - 2 x + 4 \right)}}{12} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x - 1\right)}{3} \right)}}{6}$$
The graph
The answer
[src]
___ pi*\/ 3 -------- 9
$$\frac{\sqrt{3} \pi}{9}$$
=
=
___ pi*\/ 3 -------- 9
$$\frac{\sqrt{3} \pi}{9}$$
pi*sqrt(3)/9
The graph
Use the examples entering the upper and lower limits of integration.