What is the integral of 4/3 x^{3/2} ?

The integral of 4/3 x^{3/2} is 8/15 x^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4/3 x^{3/2}

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

\frac{8}{15} x^{\frac{5}{2}} + C

Solution steps

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

Take the constant out:

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

= \frac{4}{3} \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

= \frac{4}{3} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{4}{3} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{8}{15} x^{\frac{5}{2}}

= \frac{8}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{8}{15} x^{\frac{5}{2}} + C

\int \frac{sec ^{2} ( π s )}{tan ( π s )} d s

\int 1 0^{7} e^{- a x} d x

\int (z e^{z}) d z

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

\int cos^{2} (x) tan (x) d x

What is the integral of 4/3 x^{3/2} ?
The integral of 4/3 x^{3/2} is 8/15 x^{5/2}+C