What is the integral of rcsin(x) ?

The integral of rcsin(x) is d(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 rcsin(x)

\int d arcsin (x) d x

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

Solution steps

\int d arcsin (x) d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int 7 sin^{7} (x) d x

\int (x e^{6 x}) d x

\int sin (\frac{π x}{l}) d x

\int cos (\frac{2 π x}{L}) d x

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

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