What is the integral of (2+y^3)^2 ?

The integral of (2+y^3)^2 is 4y+y^4+(y^7)/7+C

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integral of (2+y^3)^2

\int (2 + y^{3})^{2} d y

4 y + y^{4} + \frac{y ^{7}}{7} + C

Solution steps

\int (2 + y^{3})^{2} d y

Expand

(2 + y^{3})^{2} : 4 + 4 y^{3} + y^{6}

= \int 4 + 4 y^{3} + y^{6} d y

Apply the Sum Rule:

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

= \int 4 d y + \int 4 y^{3} d y + \int y^{6} d y

\int 4 d y = 4 y

\int 4 y^{3} d y = y^{4}

\int y^{6} d y = \frac{y ^{7}}{7}

= 4 y + y^{4} + \frac{y ^{7}}{7}

Add a constant to the solution

= 4 y + y^{4} + \frac{y ^{7}}{7} + C

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What is the integral of (2+y^3)^2 ?
The integral of (2+y^3)^2 is 4y+y^4+(y^7)/7+C