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

The integral of (2t^{2/3}+sqrt(t)) is 6/5 t^{5/3}+2/3 t^{3/2}+C

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integral of (2t^{2/3}+sqrt(t))

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

\frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}} + C

Solution steps

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

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

\int 2 t^{\frac{2}{3}} d t = \frac{6}{5} t^{\frac{5}{3}}

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

= \frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}}

Add a constant to the solution

= \frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}} + C

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What is the integral of (2t^{2/3}+sqrt(t)) ?
The integral of (2t^{2/3}+sqrt(t)) is 6/5 t^{5/3}+2/3 t^{3/2}+C