What is the integral of (1-x^2)^{(-1)/2} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-x^2)^{(-1)/2}

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

arcsin (x) + C

Solution steps

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

Simplify

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

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

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

Apply Trigonometric Substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = arcsin (x)

= 1 \cdot arcsin (x)

Simplify

= arcsin (x)

Add a constant to the solution

= arcsin (x) + C

\frac{\partial}{\partial s} (\frac{s - r}{t})

\frac{d}{d x} (\frac{x}{2 - x})

x^{2} + y^{2} = 25

\int \frac{8}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

x^{2} \frac{d y}{d x} + 2 x y = 5 y^{4}

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