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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of e^(x*(-3))*dx
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Integral of e^(x+e^x)
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Integral of x^(2/3)*dx
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Integral of e^(4*x)*dx
- Derivative of:
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sqrt(1-x^3)
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Identical expressions
- sqrt(one -x^ three)
- square root of (1 minus x cubed )
- square root of (one minus x to the power of three)
- √(1-x^3)
- sqrt(1-x3)
- sqrt1-x3
- sqrt(1-x³)
- sqrt(1-x to the power of 3)
- sqrt1-x^3
- sqrt(1-x^3)dx
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Similar expressions
- sqrt(1+x^3)
Integral of sqrt(1-x^3) dx
The solution
You have entered
[src]
1 / | | ________ | / 3 | \/ 1 - x dx | / 0
$$\int\limits_{0}^{1} \sqrt{1 - x^{3}}\, dx$$
Integral(sqrt(1 - x^3), (x, 0, 1))
The answer (Indefinite)
[src]
/ _ | |_ /-1/2, 1/3 | 3 2*pi*I\ | ________ x*Gamma(1/3)* | | | x *e | | / 3 2 1 \ 4/3 | / | \/ 1 - x dx = C + ------------------------------------------ | 3*Gamma(4/3) /
$$\int \sqrt{1 - x^{3}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
The graph
The answer
[src]
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|_ /-1/2, 1/3 | \
Gamma(1/3)* | | | 1|
2 1 \ 4/3 | /
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3*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
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|_ /-1/2, 1/3 | \
Gamma(1/3)* | | | 1|
2 1 \ 4/3 | /
-------------------------------
3*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 1)/(3*gamma(4/3))
The graph
Use the examples entering the upper and lower limits of integration.