What is the integral of \sqrt[3]{x}(x+1)^2 ?

The integral of \sqrt[3]{x}(x+1)^2 is 3/10 x^{10/3}+6/7 x^{7/3}+3/4 x^{4/3}+C

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integral of \sqrt[3]{x}(x+1)^2

\frac{3}{10} x^{\frac{10}{3}} + \frac{6}{7} x^{\frac{7}{3}} + \frac{3}{4} x^{\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 x^{\frac{7}{3}} d x = \frac{3}{10} x^{\frac{10}{3}}

\int 2 x^{\frac{4}{3}} d x = \frac{6}{7} x^{\frac{7}{3}}

= \frac{3}{10} x^{\frac{10}{3}} + \frac{6}{7} x^{\frac{7}{3}} + \frac{3}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{10} x^{\frac{10}{3}} + \frac{6}{7} x^{\frac{7}{3}} + \frac{3}{4} x^{\frac{4}{3}} + C

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

f (x) = x sin (x), 0, 2 π

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

f (x) = x - 5

y^{^{''}} + 2 y^{^{'}} + y = sin (x) + 4 cos (2 x)

What is the integral of \sqrt[3]{x}(x+1)^2 ?
The integral of \sqrt[3]{x}(x+1)^2 is 3/10 x^{10/3}+6/7 x^{7/3}+3/4 x^{4/3}+C