What is the integral of (x^2)arcsin(x) ?

The integral of (x^2)arcsin(x) is 1/3 x^3arcsin(x)-1/3 (1/3 (1-x^2)^{3/2}-sqrt(1-x^2))+C

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integral of (x^2)arcsin(x)

\int (x^{2}) arcsin (x) d x

\frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

Solution steps

\int x^{2} arcsin (x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} arcsin (x) - \int \frac{x ^{3}}{3 1 - x ^{2}} d x

= \frac{1}{3} x^{3} arcsin (x) - \int \frac{x ^{3}}{3 1 - x ^{2}} d x

\int \frac{x ^{3}}{3 1 - x ^{2}} d x = \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

= \frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

Add a constant to the solution

= \frac{1}{3} x^{3} arcsin (x) - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

\frac{\partial}{\partial y} (\frac{4 x - 4 z}{y + 4 z})

\int (2 y^{2}) d y

\int \frac{r}{a ^{2} - r ^{2}} d r

\int_{- 1}^{2} x (1 + x^{3}) d x

\frac{d}{d x} (\frac{1}{10} (x - 60)^{2} + 100)

What is the integral of (x^2)arcsin(x) ?
The integral of (x^2)arcsin(x) is 1/3 x^3arcsin(x)-1/3 (1/3 (1-x^2)^{3/2}-sqrt(1-x^2))+C