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

\frac{\partial}{\partial x} (- 4 x^{2})

(- e^{x})^{^{'}}

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{- y}

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

\frac{d}{d x} (x + 10)

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