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

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

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integral of (arcsin(x))/(x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x + 2)

9 x, x^{3}

\int u^{- 5} (8 - u^{5} + u^{10}) d u

n \to \infty lim ((n + 1) x)

\frac{3 x - 9}{2 x + 8}

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