What is the integral of (2arcsin(x))/(sqrt(1-x^2)) ?

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

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integral of (2arcsin(x))/(sqrt(1-x^2))

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

arcsin^{2} (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 2 \cdot \frac{u ^{2}}{2}

Substitute back

u = arcsin (x)

= 2 \cdot \frac{arcsin ^{2} ( x )}{2}

Simplify

2 \cdot \frac{arcsin ^{2} ( x )}{2} : arcsin^{2} (x)

= arcsin^{2} (x)

Add a constant to the solution

= arcsin^{2} (x) + C

2 x^{2} - 2 x + C

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