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

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

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integral of arcsin^2(x)

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

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

Solution steps

\int arcsin^{2} (x) 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

f (x) = \frac{x ^{2}}{x - 11}

x \to \infty lim (\frac{e ^{5 x}}{9 x ^{4} + 31 x + 1})

\frac{d}{d x} (sec^{2} (2 x + 4) \cdot 2)

f (x) = \frac{f ( x )}{x ^{7}}

5 x^{3} + 2 x^{2} + 3

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