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

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

Popular >

integral of ((2x)/3)^2

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

\frac{4 x ^{3}}{27} + C

Solution steps

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

Simplify

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

= \int \frac{4 x ^{2}}{9} d x

Take the constant out:

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

= \frac{4}{9} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{4}{9} \cdot \frac{x ^{3}}{3}

Simplify

\frac{4}{9} \cdot \frac{x ^{3}}{3} : \frac{4 x ^{3}}{27}

= \frac{4 x ^{3}}{27}

Add a constant to the solution

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

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

\int \frac{1}{x} \cdot \frac{x - a}{x + a} d x

\int \frac{2 v}{v ^{2} - b ^{4}} d v

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

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

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