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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^2*e^(x*(-2))
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Integral of e^(-x^3)
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Integral of -exp(-3*x)
- Integral of (xcosx)/(2+3x^3)
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Identical expressions
- x*(x^ three + one)^(one / three)
- x multiply by (x cubed plus 1) to the power of (1 divide by 3)
- x multiply by (x to the power of three plus one) to the power of (one divide by three)
- x*(x3+1)(1/3)
- x*x3+11/3
- x*(x³+1)^(1/3)
- x*(x to the power of 3+1) to the power of (1/3)
- x(x^3+1)^(1/3)
- x(x3+1)(1/3)
- xx3+11/3
- xx^3+1^1/3
- x*(x^3+1)^(1 divide by 3)
- x*(x^3+1)^(1/3)dx
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Similar expressions
- x*(x^3-1)^(1/3)
Integral of x*(x^3+1)^(1/3) dx
The solution
You have entered
[src]
1 / | | ________ | 3 / 3 | x*\/ x + 1 dx | / 0
$$\int\limits_{0}^{1} x \sqrt[3]{x^{3} + 1}\, dx$$
Integral(x*(x^3 + 1)^(1/3), (x, 0, 1))
The answer (Indefinite)
[src]
/ _ | 2 |_ /-1/3, 2/3 | 3 pi*I\ | ________ x *Gamma(2/3)* | | | x *e | | 3 / 3 2 1 \ 5/3 | / | x*\/ x + 1 dx = C + ----------------------------------------- | 3*Gamma(5/3) /
$$\int x \sqrt[3]{x^{3} + 1}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
The graph
The answer
[src]
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|_ /-1/3, 2/3 | \
Gamma(2/3)* | | | -1|
2 1 \ 5/3 | /
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3*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
=
=
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|_ /-1/3, 2/3 | \
Gamma(2/3)* | | | -1|
2 1 \ 5/3 | /
--------------------------------
3*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
gamma(2/3)*hyper((-1/3, 2/3), (5/3,), -1)/(3*gamma(5/3))
The graph
Use the examples entering the upper and lower limits of integration.