What is the integral of 4arcsin(x) ?

The integral of 4arcsin(x) is 4(xarcsin(x)+sqrt(1-x^2))+C

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integral of 4arcsin(x)

\int 4 arcsin (x) d x

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

Solution steps

\int 4 arcsin (x) d x

Take the constant out:

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

= 4 \cdot \int arcsin (x) d x

Apply Integration By Parts

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

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

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

Simplify

= 4 (x arcsin (x) + 1 - x^{2})

Add a constant to the solution

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

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