What is the integral of (3x^2+9)^2 ?

The integral of (3x^2+9)^2 is (9x^5)/5+18x^3+81x+C

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integral of (3x^2+9)^2

\int (3 x^{2} + 9)^{2} d x

\frac{9 x ^{5}}{5} + 18 x^{3} + 81 x + C

Solution steps

\int (3 x^{2} + 9)^{2} d x

Expand

(3 x^{2} + 9)^{2} : 9 x^{4} + 54 x^{2} + 81

= \int 9 x^{4} + 54 x^{2} + 81 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^{4} d x + \int 54 x^{2} d x + \int 81 d x

\int 9 x^{4} d x = \frac{9 x ^{5}}{5}

\int 54 x^{2} d x = 18 x^{3}

\int 81 d x = 81 x

= \frac{9 x ^{5}}{5} + 18 x^{3} + 81 x

Add a constant to the solution

= \frac{9 x ^{5}}{5} + 18 x^{3} + 81 x + C

f (r) = 4 π r^{2}

- 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 9

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

(3, 2), (- 3, - 2)

A e^{x}

What is the integral of (3x^2+9)^2 ?
The integral of (3x^2+9)^2 is (9x^5)/5+18x^3+81x+C