What is the integral of (x^2)/(5x^3+2) ?

The integral of (x^2)/(5x^3+2) is 1/15 ln|5x^3+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^2)/(5x^3+2)

\int \frac{x ^{2}}{5 x ^{3} + 2} d x

\frac{1}{15} ln 5 x^{3} + 2 + C

Solution steps

\int \frac{x ^{2}}{5 x ^{3} + 2} d x

Apply u-substitution

: \int \frac{1}{15 u} d u

= \int \frac{1}{15 u} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{15} ln ∣ u ∣

Substitute back

u = 5 x^{3} + 2

= \frac{1}{15} ln 5 x^{3} + 2

Add a constant to the solution

= \frac{1}{15} ln 5 x^{3} + 2 + C

(x + 1) y^{^{'}} = x y

\frac{d}{d x} (cos (x) + cos (2 x))

f (x) = x^{2} - 2 x + 1, (1, 4)

\int \frac{( 2 r + 1 )}{( r ^{2} - 3 r + 2 )} d r

x d y - y d x = 0

What is the integral of (x^2)/(5x^3+2) ?
The integral of (x^2)/(5x^3+2) is 1/15 ln|5x^3+2|+C