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How to use it?
- Integral of d{x}:
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Integral of cosx
- Integral of (3-sin(x))/(2cos(x)+3tan(x))
- Integral of (x^3+y)^1/2dx
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Integral of (x^3dx)/(cos^2(x^4))
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Identical expressions
- (x^ three +y)^ one /2dx
- (x cubed plus y) to the power of 1 divide by 2dx
- (x to the power of three plus y) to the power of one divide by 2dx
- (x3+y)1/2dx
- x3+y1/2dx
- (x³+y)^1/2dx
- (x to the power of 3+y) to the power of 1/2dx
- x^3+y^1/2dx
- (x^3+y)^1 divide by 2dx
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Similar expressions
- (x^3-y)^1/2dx
Integral of (x^3+y)^1/2dx dx
The solution
You have entered
[src]
1 / | | ________ | / 3 | \/ x + y dx | / 0
$$\int\limits_{0}^{1} \sqrt{x^{3} + y}\, dx$$
Integral(sqrt(x^3 + y), (x, 0, 1))
The answer (Indefinite)
[src]
/ _ / | 3 pi*I\ | ___ |_ |-1/2, 1/3 | x *e | | ________ x*\/ y *Gamma(1/3)* | | | --------| | / 3 2 1 \ 4/3 | y / | \/ x + y dx = C + ---------------------------------------------- | 3*Gamma(4/3) /
$$\int \sqrt{x^{3} + y}\, dx = C + \frac{x \sqrt{y} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{y}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
The answer
[src]
_ / | pi*I\
___ |_ |-1/2, 1/3 | e |
\/ y *Gamma(1/3)* | | | -----|
2 1 \ 4/3 | y /
-----------------------------------------
3*Gamma(4/3)
$$\frac{\sqrt{y} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{e^{i \pi}}{y}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_ / | pi*I\
___ |_ |-1/2, 1/3 | e |
\/ y *Gamma(1/3)* | | | -----|
2 1 \ 4/3 | y /
-----------------------------------------
3*Gamma(4/3)
$$\frac{\sqrt{y} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{e^{i \pi}}{y}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
sqrt(y)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), exp_polar(pi*i)/y)/(3*gamma(4/3))
Use the examples entering the upper and lower limits of integration.