What is the integral of arcsin(y) ?

The integral of arcsin(y) is yarcsin(y)+sqrt(1-y^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(y)

\int arcsin (y) d y

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

Solution steps

\int arcsin (y) d y

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int_{- \infty}^{0} \frac{1}{1 + x ^{2}} d x

\frac{d}{d x} (ln (5 x + 1))

f (x) = \frac{19}{x ^{5}}

\frac{d}{d x} (- 2 lo g_{6} (x))

e^{9 x}

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