What is the integral of \sqrt[3]{t}(t+1)^3 ?

The integral of \sqrt[3]{t}(t+1)^3 is 3/13 t^{13/3}+9/10 t^{10/3}+9/7 t^{7/3}+3/4 t^{4/3}+C

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integral of \sqrt[3]{t}(t+1)^3

\frac{3}{13} t^{\frac{13}{3}} + \frac{9}{10} t^{\frac{10}{3}} + \frac{9}{7} t^{\frac{7}{3}} + \frac{3}{4} t^{\frac{4}{3}} + C

Solution steps

Expand

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^{\frac{10}{3}} d t = \frac{3}{13} t^{\frac{13}{3}}

\int 3 t^{\frac{7}{3}} d t = \frac{9}{10} t^{\frac{10}{3}}

\int 3 t^{\frac{4}{3}} d t = \frac{9}{7} t^{\frac{7}{3}}

= \frac{3}{13} t^{\frac{13}{3}} + \frac{9}{10} t^{\frac{10}{3}} + \frac{9}{7} t^{\frac{7}{3}} + \frac{3}{4} t^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{13} t^{\frac{13}{3}} + \frac{9}{10} t^{\frac{10}{3}} + \frac{9}{7} t^{\frac{7}{3}} + \frac{3}{4} t^{\frac{4}{3}} + C

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What is the integral of \sqrt[3]{t}(t+1)^3 ?
The integral of \sqrt[3]{t}(t+1)^3 is 3/13 t^{13/3}+9/10 t^{10/3}+9/7 t^{7/3}+3/4 t^{4/3}+C