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- Integral of d{x}:
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Integral of 1/(1-x^3)
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Integral of dx/(e^x-1)
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Integral of cos(x)*cos(x)
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Integral of dx/sin^64x
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Identical expressions
- sqrt(one -x)arcsin(sqrt(x))
- square root of (1 minus x)arc sinus of ( square root of (x))
- square root of (one minus x)arc sinus of ( square root of (x))
- √(1-x)arcsin(√(x))
- sqrt1-xarcsinsqrtx
- sqrt(1-x)arcsin(sqrt(x))dx
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Similar expressions
- sqrt(1+x)arcsin(sqrt(x))
- 1/(sqrt(1-x)*arcsin(sqrt(x)))
Integral of sqrt(1-x)arcsin(sqrt(x)) dx
The solution
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1 / | | _______ / ___\ | \/ 1 - x *asin\\/ x / dx | / 3/4
$$\int\limits_{\frac{3}{4}}^{1} \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}\, dx$$
Integral(sqrt(1 - x)*asin(sqrt(x)), (x, 3/4, 1))
The answer (Indefinite)
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// 3/2 \
|| ___ x |
/ 2*|<- \/ x + ---- for And(x <= 1, x > 0)|
| || 3 | 3/2 / ___\
| _______ / ___\ \\ / 2*(1 - x) *asin\\/ x /
| \/ 1 - x *asin\\/ x / dx = C - ------------------------------------------- - ------------------------
| 3 3
/
$$\int \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}\, dx = C - \frac{2 \left(1 - x\right)^{\frac{3}{2}} \operatorname{asin}{\left(\sqrt{x} \right)}}{3} - \frac{2 \left(\begin{cases} \frac{x^{\frac{3}{2}}}{3} - \sqrt{x} & \text{for}\: x \leq 1 \wedge x > 0 \end{cases}\right)}{3}$$
The graph
The answer
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___ 4 \/ 3 pi - - ----- + -- 9 4 36
$$- \frac{\sqrt{3}}{4} + \frac{\pi}{36} + \frac{4}{9}$$
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=
___ 4 \/ 3 pi - - ----- + -- 9 4 36
$$- \frac{\sqrt{3}}{4} + \frac{\pi}{36} + \frac{4}{9}$$
4/9 - sqrt(3)/4 + pi/36
Use the examples entering the upper and lower limits of integration.