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

The integral of (3x^3+2)^2 is (9x^7)/7+3x^4+4x+C

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integral of (3x^3+2)^2

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

\frac{9 x ^{7}}{7} + 3 x^{4} + 4 x + C

Solution steps

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

Expand

(3 x^{3} + 2)^{2} : 9 x^{6} + 12 x^{3} + 4

= \int 9 x^{6} + 12 x^{3} + 4 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 9 x^{6} d x + \int 12 x^{3} d x + \int 4 d x

\int 9 x^{6} d x = \frac{9 x ^{7}}{7}

\int 12 x^{3} d x = 3 x^{4}

\int 4 d x = 4 x

= \frac{9 x ^{7}}{7} + 3 x^{4} + 4 x

Add a constant to the solution

= \frac{9 x ^{7}}{7} + 3 x^{4} + 4 x + C

What is the integral of (3x^3+2)^2 ?
The integral of (3x^3+2)^2 is (9x^7)/7+3x^4+4x+C