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

The integral of sqrt((arcsin(x))/(1-x^2)) is 2/3 arcsin^{3/2}(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt((arcsin(x))/(1-x^2))

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

\frac{2}{3} arcsin^{\frac{3}{2}} (x) + C

Solution steps

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

Simplify

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

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

Apply u-substitution

: \int 2 u^{2} d u

= \int 2 u^{2} d u

Take the constant out:

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

= 2 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 2 \cdot \frac{u ^{3}}{3}

Substitute back

u = arcsin (x)

= 2 \cdot \frac{( arcsin ( x ) ) ^{3}}{3}

Simplify

2 \cdot \frac{( arcsin ( x ) ) ^{3}}{3} : \frac{2}{3} arcsin^{\frac{3}{2}} (x)

= \frac{2}{3} arcsin^{\frac{3}{2}} (x)

Add a constant to the solution

= \frac{2}{3} arcsin^{\frac{3}{2}} (x) + C

x \to 4 lim (\frac{∣ x - 4 ∣}{x - 4})

\int e^{- s t - t} d t

\frac{d}{d x} (cos (x) x^{3})

\int (2 x + 9)^{5} d x

f (x) = \frac{4 x ^{2}}{x + 3}, (1, 1)

What is the integral of sqrt((arcsin(x))/(1-x^2)) ?
The integral of sqrt((arcsin(x))/(1-x^2)) is 2/3 arcsin^{3/2}(x)+C