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

The integral of (2x^2)/5 is (2x^3)/(15)+C

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integral of (2x^2)/5

integral

\frac{2 x ^{2}}{5}

\frac{2 x ^{3}}{15} + C

Solution steps

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

Take the constant out:

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

= \frac{2}{5} \cdot \int x^{2} d x

Apply the Power Rule

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

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

Simplify

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

= \frac{2 x ^{3}}{15}

Add a constant to the solution

= \frac{2 x ^{3}}{15} + C

(a + b)^{- 2}

\frac{x}{1 - x}

\frac{- x}{( 1 + x )}

(1 - t^{2})^{3}

\frac{5 x ^{4}}{x ^{5} + 9}