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Popular >

integral of 2/3 x^2

Solution

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

Solution

\frac{2 x ^{3}}{9} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

\frac{2}{3} \cdot \frac{x ^{3}}{3} : \frac{2 x ^{3}}{9}

= \frac{2 x ^{3}}{9}

Add a constant to the solution

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

Popular Examples

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

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

y^'+4y=3sin(e^4x)

y^{^{'}} + 4 y = 3 sin (e^{4} x)

integral of x^m

\int x^{m} d x

integral of 1/(x^4+4x^2)

\int \frac{1}{x ^{4} + 4 x ^{2}} d x

y^{''}+2y^'+5y=4e^{-t}cos(2t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{- t} cos (2 t)

Frequently Asked Questions (FAQ)

What is the integral of 2/3 x^2 ?
The integral of 2/3 x^2 is (2x^3)/9+C