What is the integral of x/(x^2-7) ?

The integral of x/(x^2-7) is 1/2 ln|x^2-7|+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^2-7)

\int \frac{x}{x ^{2} - 7} d x

\frac{1}{2} ln x^{2} - 7 + C

Solution steps

\int \frac{x}{x ^{2} - 7} 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 = x^{2} - 7

= \frac{1}{2} ln x^{2} - 7

Add a constant to the solution

= \frac{1}{2} ln x^{2} - 7 + C

\int \frac{3 x ^{2}}{( 8 - 3 x ^{3} ) ^{5}} d x

\int - cos (x) x d x

\int \frac{8}{x ln ( 9 x )} d x

\int \frac{1}{a x - b x ^{2}} d x

\int (12 x^{- 1} - 6 x^{4} - 9 x^{2} + 5 x - 15) d x

What is the integral of x/(x^2-7) ?
The integral of x/(x^2-7) is 1/2 ln|x^2-7|+C