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

The integral of (x^2)/(sqrt(x^3+5)) is 2/3 sqrt(x^3+5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^2)/(sqrt(x^3+5))

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

\frac{2}{3} x^{3} + 5 + C

Solution steps

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

Apply u-substitution

= \int \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{2}{3} u

Substitute back

u = x^{3} + 5

= \frac{2}{3} x^{3} + 5

Add a constant to the solution

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

\int x^{- 3} arctan (x) d x

\int \frac{4}{x ( ln ( x ) ) ^{4}} d x

\int 1 + y^{4} d y

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

\int \frac{e ^{3 x}}{e ^{2 x} + 1} d x

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