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

The integral of x/(7x^2-2) is 1/14 ln|7x^2-2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x/(7x^2-2)

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

\frac{1}{14} ln 7 x^{2} - 2 + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} ln ∣ u ∣

Substitute back

u = 7 x^{2} - 2

= \frac{1}{14} ln 7 x^{2} - 2

Add a constant to the solution

= \frac{1}{14} ln 7 x^{2} - 2 + C

\int x^{2} (5 + 2 x^{3}) d x

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

\int \frac{x ^{2}}{x ^{3} + 4 x ^{2} + 6 x} d x

\int (tan (x) + x^{- 1} - 2 x + 3) d x

\int \frac{1}{100 + 2 x} d x

What is the integral of x/(7x^2-2) ?
The integral of x/(7x^2-2) is 1/14 ln|7x^2-2|+C