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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

integral

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

- \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{2 y ^{2}}{x ^{3}}

x^{5} (1 - x^{2})^{0.5}

(x^{2} - 1)^{2}

(1 - 4 x) (1 + x)

3 - 2 (x)^{- 1}

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