What is the integral of x^2sqrt(3x^3+4) ?

The integral of x^2sqrt(3x^3+4) is 2/27 (3x^3+4)^{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^2sqrt(3x^3+4)

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

\frac{2}{27} (3 x^{3} + 4)^{\frac{3}{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{u}{9} d u

= \int \frac{u}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{9} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 3 x^{3} + 4

= \frac{1}{9} \cdot \frac{2}{3} (3 x^{3} + 4)^{\frac{3}{2}}

Simplify

\frac{1}{9} \cdot \frac{2}{3} (3 x^{3} + 4)^{\frac{3}{2}} : \frac{2}{27} (3 x^{3} + 4)^{\frac{3}{2}}

= \frac{2}{27} (3 x^{3} + 4)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{27} (3 x^{3} + 4)^{\frac{3}{2}} + C

\int ln (25 x) d x

\int \frac{1}{( x + 2 ) ( 3 x + 4 )} d x

\int 12 e^{- 3 x} d x

\int e^{2 x} - 6 x d x

\int \frac{1}{x} ln (x) d x

What is the integral of x^2sqrt(3x^3+4) ?
The integral of x^2sqrt(3x^3+4) is 2/27 (3x^3+4)^{3/2}+C