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

The integral of x/(x^2-y^2) is 1/2 ln|-y^2+x^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/(x^2-y^2)

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

\frac{1}{2} ln - y^{2} + x^{2} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = - y^{2} + x^{2}

= \frac{1}{2} ln - y^{2} + x^{2}

Add a constant to the solution

= \frac{1}{2} ln - y^{2} + x^{2} + C

\int \frac{x ^{2} + 21}{x ^{2} + 25} d x

\int x^{2} - 11 d x

\int e^{3 x} + \frac{1}{x ^{3}} - 7 x^{\frac{3}{2}} d x

x^{- 3}

\int cot (x) e^{l n (s i n (x))} d x

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