What is the integral of arcsin(x)x ?

The integral of arcsin(x)x is 1/2 x^2arcsin(x)-1/4 (arcsin(x)-1/2 sin(2arcsin(x)))+C

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integral of arcsin(x)x

\int arcsin (x) x d x

\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

Solution steps

\int arcsin (x) x d x

Apply Integration By Parts

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

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

\int \frac{x ^{2}}{2 1 - x ^{2}} d x = \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= \frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

Add a constant to the solution

= \frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

x \to - 3 lim (2 x^{3} + 5 x^{2} - 25)

y^{^{'}} = \frac{2 y}{x}, y (1) = 2

\int_{0}^{1} \frac{x}{e ^{2 x}} d x

- 9.8 x^{2} + 2 x + 1

x y^{^{'}} + 5 y = 7 x^{2}

What is the integral of arcsin(x)x ?
The integral of arcsin(x)x is 1/2 x^2arcsin(x)-1/4 (arcsin(x)-1/2 sin(2arcsin(x)))+C