What is the integral of (5x^2+9)^2 ?

The integral of (5x^2+9)^2 is 5x^5+30x^3+81x+C

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integral of (5x^2+9)^2

\int (5 x^{2} + 9)^{2} d x

5 x^{5} + 30 x^{3} + 81 x + C

Solution steps

\int (5 x^{2} + 9)^{2} d x

Expand

(5 x^{2} + 9)^{2} : 25 x^{4} + 90 x^{2} + 81

= \int 25 x^{4} + 90 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 25 x^{4} d x + \int 90 x^{2} d x + \int 81 d x

\int 25 x^{4} d x = 5 x^{5}

\int 90 x^{2} d x = 30 x^{3}

\int 81 d x = 81 x

= 5 x^{5} + 30 x^{3} + 81 x

Add a constant to the solution

= 5 x^{5} + 30 x^{3} + 81 x + C

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What is the integral of (5x^2+9)^2 ?
The integral of (5x^2+9)^2 is 5x^5+30x^3+81x+C