What is the integral of (x^3+4)^2 ?

The integral of (x^3+4)^2 is (x^7)/7+2x^4+16x+C

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integral of (x^3+4)^2

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

\frac{x ^{7}}{7} + 2 x^{4} + 16 x + C

Solution steps

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

Expand

(x^{3} + 4)^{2} : x^{6} + 8 x^{3} + 16

= \int x^{6} + 8 x^{3} + 16 d x

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^{6} d x + \int 8 x^{3} d x + \int 16 d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 16 d x = 16 x

= \frac{x ^{7}}{7} + 2 x^{4} + 16 x

Add a constant to the solution

= \frac{x ^{7}}{7} + 2 x^{4} + 16 x + C

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What is the integral of (x^3+4)^2 ?
The integral of (x^3+4)^2 is (x^7)/7+2x^4+16x+C