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

\int \frac{x ^{2}}{x + 7} d x

y^{^{''}} - 2 y^{^{'}} - 15 y = e^{3 x} cos (2 x)

\frac{d}{d x} (2 x - 7)

\int cos^{5} (t) d t

cos (π - 6 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