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

The integral of 2sqrt(x^3)+9\sqrt[3]{x^2} is 4/5 x^{5/2}+27/5 x^{5/3}+C

Popular >

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

\int 2 x^{3} + 9 3 x^{2} d x

\frac{4}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}} + C

Solution steps

\int 2 x^{3} + 9 3 x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{3} d x + \int 9 3 x^{2} d x

\int 2 x^{3} d x = \frac{4}{5} x^{\frac{5}{2}}

\int 9 3 x^{2} d x = \frac{27}{5} x^{\frac{5}{3}}

= \frac{4}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}} + C

\int sec^{2} (2 x - 3) d x

\int e^{- s x} cos (a x) d x

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

\int \frac{sec ^{2} ( x )}{9 + tan ^{2} ( x )} d x

\int (x^{2} + 2)^{4} d x

What is the integral of 2sqrt(x^3)+9\sqrt[3]{x^2} ?
The integral of 2sqrt(x^3)+9\sqrt[3]{x^2} is 4/5 x^{5/2}+27/5 x^{5/3}+C