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

The integral of (sqrt(t^3)+\sqrt[3]{t^2}) is 2/5 t^{5/2}+3/5 t^{5/3}+C

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

\frac{2}{5} t^{\frac{5}{2}} + \frac{3}{5} t^{\frac{5}{3}} + C

Solution steps

Apply the Sum Rule:

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

\int t^{3} d t = \frac{2}{5} t^{\frac{5}{2}}

= \frac{2}{5} t^{\frac{5}{2}} + \frac{3}{5} t^{\frac{5}{3}}

Add a constant to the solution

= \frac{2}{5} t^{\frac{5}{2}} + \frac{3}{5} t^{\frac{5}{3}} + C

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