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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of e^x/x^2
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Integral of sin(x)^2*cos(x)^4
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Integral of x*ln(x+1)dx
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Integral of 1/(2-x)
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Identical expressions
- sqrt(x)/sqrt(one -x^ three)
- square root of (x) divide by square root of (1 minus x cubed )
- square root of (x) divide by square root of (one minus x to the power of three)
- √(x)/√(1-x^3)
- sqrt(x)/sqrt(1-x3)
- sqrtx/sqrt1-x3
- sqrt(x)/sqrt(1-x³)
- sqrt(x)/sqrt(1-x to the power of 3)
- sqrtx/sqrt1-x^3
- sqrt(x) divide by sqrt(1-x^3)
- sqrt(x)/sqrt(1-x^3)dx
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Similar expressions
- sqrt(x)/sqrt(1+x^3)
Integral of sqrt(x)/sqrt(1-x^3) dx
The solution
You have entered
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1 / | | ___ | \/ x | ----------- dx | ________ | / 3 | \/ 1 - x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{\sqrt{- x^{3} + 1}}\, dx$$
Integral(sqrt(x)/(sqrt(1 - x^3)), (x, 0, 1))
The answer (Indefinite)
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/ // / 3/2\ \ | ||-2*I*acosh\x / | 3| | | ___ ||---------------- for |x | > 1| | \/ x || 3 | | ----------- dx = C + |< | | ________ || / 3/2\ | | / 3 || 2*asin\x / | | \/ 1 - x || ------------ otherwise | | \\ 3 / /
$$-{{2\,\arctan \left({{\sqrt{1-x^3}}\over{x^{{{3}\over{2}}}}}\right)
}\over{3}}$$
The graph
The answer
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1 / | | / ___ | | -I*\/ x 3 | |---------------------------- for x > 1 | | __________ ___________ | | / 3/2 / 3/2 | |\/ 1 + x *\/ -1 + x | < dx | | ___ | | \/ x | | ----------- otherwise | | ________ | | / 3 | \ \/ 1 - x | / 0
$${{\pi}\over{3}}$$
=
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1 / | | / ___ | | -I*\/ x 3 | |---------------------------- for x > 1 | | __________ ___________ | | / 3/2 / 3/2 | |\/ 1 + x *\/ -1 + x | < dx | | ___ | | \/ x | | ----------- otherwise | | ________ | | / 3 | \ \/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i \sqrt{x}}{\sqrt{x^{\frac{3}{2}} - 1} \sqrt{x^{\frac{3}{2}} + 1}} & \text{for}\: x^{3} > 1 \\\frac{\sqrt{x}}{\sqrt{- x^{3} + 1}} & \text{otherwise} \end{cases}\, dx$$
The graph
Use the examples entering the upper and lower limits of integration.