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

The integral of (x^2)/((1-y^2)) is (x^3)/(3(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 (x^2)/((1-y^2))

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

\frac{x ^{3}}{3 ( 1 - y ^{2} )} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{1 - y ^{2}} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{1 - y ^{2}} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 ( 1 - y ^{2} )}

= \frac{x ^{3}}{3 ( 1 - y ^{2} )}

Add a constant to the solution

= \frac{x ^{3}}{3 ( 1 - y ^{2} )} + C

e^{a x}

\int (\frac{4}{x} - \frac{16}{x ^{2}}) d x

\frac{\partial}{\partial y} (\frac{e ^{y}}{x + y ^{9}})

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

f (x) = cos (x) - sin (x)

What is the integral of (x^2)/((1-y^2)) ?
The integral of (x^2)/((1-y^2)) is (x^3)/(3(1-y^2))+C