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

The integral of (arcsin(x))^2 is xarcsin^2(x)-2(-arcsin(x)sqrt(1-x^2)+x)+C

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integral of (arcsin(x))^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

= x arcsin^{2} (x) - 2 (- arcsin (x) 1 - x^{2} + x)

Add a constant to the solution

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

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

\frac{d y}{d x} = x + x y^{2}

f (x) = x^{3 x}

(t + 2 y + 3) + (2 t + 4 y - 1) \frac{d y}{d t} = 0

y^{^{''}} - \frac{1}{x} y^{^{'}} + \frac{1}{x ^{2}} y = \frac{2}{x}

What is the integral of (arcsin(x))^2 ?
The integral of (arcsin(x))^2 is xarcsin^2(x)-2(-arcsin(x)sqrt(1-x^2)+x)+C