What is the integral of x/((2x^2-5)) ?

The integral of x/((2x^2-5)) is 1/4 ln|2x^2-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/((2x^2-5))

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

\frac{1}{4} ln 2 x^{2} - 5 + C

Solution steps

\int \frac{x}{2 x ^{2} - 5} d x

Apply u-substitution

: \int \frac{1}{4 u} d u

= \int \frac{1}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = 2 x^{2} - 5

= \frac{1}{4} ln 2 x^{2} - 5

Add a constant to the solution

= \frac{1}{4} ln 2 x^{2} - 5 + C

\int \frac{x ^{2}}{12 - 5 x ^{3}} d x

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

\int 2 x \cdot \frac{1}{x} d x

\int 12 sec (4 x) tan (4 x) d x

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

What is the integral of x/((2x^2-5)) ?
The integral of x/((2x^2-5)) is 1/4 ln|2x^2-5|+C