What is the integral of 3xarcsin(x) ?

The integral of 3xarcsin(x) is 3(1/2 x^2arcsin(x)-1/4 (arcsin(x)-1/2 sin(2arcsin(x))))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3xarcsin(x)

\int 3 x arcsin (x) d x

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

Solution steps

\int 3 x arcsin (x) d x

Take the constant out:

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

= 3 \cdot \int x arcsin (x) d x

Apply Integration By Parts

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

= 3 (\frac{1}{2} x^{2} arcsin (x) - \int \frac{x ^{2}}{2 1 - x ^{2}} d x)

\int \frac{x ^{2}}{2 1 - x ^{2}} d x = \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= 3 (\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))))

Add a constant to the solution

= 3 (\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))) + C

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

\int \frac{e ^{3 x} + 3 e ^{x} + 3}{e ^{x}} d x

\int \frac{( y - 3 )}{4 y} d y

\int 5 x^{- 3} + 8 x^{- 2} + 2 x^{- 1} d x

What is the integral of 3xarcsin(x) ?
The integral of 3xarcsin(x) is 3(1/2 x^2arcsin(x)-1/4 (arcsin(x)-1/2 sin(2arcsin(x))))+C