What is the integral of (arcsin(x)) ?

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

\int (arcsin (x)) d x

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

Solution steps

\int arcsin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{sin ( 2 x )}{1 + 3 sin ^{2} ( x )} d x

y^{^{'}} = sin (x + y)

\frac{d}{d t} (e^{9 t s i n (2 t)})

y^{^{''}} + 4 y^{^{'}} = t^{2} + 3 e^{t}

\int e^{- v} cos (w v) d v

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