What is the integral of (3+2x^2)/(\sqrt[4]{9x+2x^3)} ?

The integral of (3+2x^2)/(\sqrt[4]{9x+2x^3)} is 4/9 (9x+2x^3)^{3/4}+C

Popular >

integral of (3+2x^2)/(\sqrt[4]{9x+2x^3)}

\frac{4}{9} (9 x + 2 x^{3})^{\frac{3}{4}} + C

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{4}{3} u^{\frac{3}{4}}

= \frac{1}{3} \cdot \frac{4}{3} u^{\frac{3}{4}}

Substitute back

u = 9 x + 2 x^{3}

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{ln ( tan ( x ) )}{cos ( x ) sin ( x )} d x

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

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

\int \frac{ln ( tan ( x ) )}{sin ( x ) cos ( x )} d x

\int \frac{arctan ( x )}{x ^{2} ( 1 + x ^{2} )} d x

What is the integral of (3+2x^2)/(\sqrt[4]{9x+2x^3)} ?
The integral of (3+2x^2)/(\sqrt[4]{9x+2x^3)} is 4/9 (9x+2x^3)^{3/4}+C