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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{u ^{2}}{2}

Substitute back

u = arcsin (x)

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

Simplify

\frac{1}{2} \cdot \frac{arcsin ^{2} ( x )}{2} : \frac{1}{4} arcsin^{2} (x)

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

Add a constant to the solution

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

\int cos (10 x) cos (7 x) d x

\int \frac{sin ( x )}{9 + cos ^{2} ( x )} d x

\int \frac{sec ( x )}{tan ^{3} ( x )} d x

\int \frac{sec ^{2} ( 3 ) x}{x} d x

\int - 6 x^{2} + 24 x d x

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