Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of x^e
-
Integral of sin(x²)
-
Integral of 1/(x³+1)
- Integral of ln(x+(1+x^2)^(1/2))
- How do you in partial fractions?:
- x/(x^3+1)
-
Identical expressions
- x/(x^ three + one)
- x divide by (x cubed plus 1)
- x divide by (x to the power of three plus 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
-
Similar expressions
- x/(x^3-1)
- e^(acot(x))/(x^3+1)
Integral of x/(x^3+1) dx
The solution
You have entered
[src]
oo / | | x | ------ dx | 3 | x + 1 | / 0
$$\int\limits_{0}^{\infty} \frac{x}{x^{3} + 1}\, dx$$
Integral(x/(x^3 + 1), (x, 0, oo))
The answer (Indefinite)
[src]
/ ___ \ / ___ |2*\/ 3 *(-1/2 + x)| | / 2 \ \/ 3 *atan|------------------| | x log(1 + x) log\1 + x - x/ \ 3 / | ------ dx = C - ---------- + --------------- + ------------------------------ | 3 3 6 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 graph
The answer
[src]
___
2*pi*\/ 3
----------
9
$$\frac{2 \sqrt{3} \pi}{9}$$
=
=
___
2*pi*\/ 3
----------
9
$$\frac{2 \sqrt{3} \pi}{9}$$
2*pi*sqrt(3)/9
The graph
Use the examples entering the upper and lower limits of integration.