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

The integral of x^2(2x+5)^2 is (4x^5)/5+5x^4+(25x^3)/3+C

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

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

\frac{4 x ^{5}}{5} + 5 x^{4} + \frac{25 x ^{3}}{3} + C

Solution steps

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

Expand

x^{2} (2 x + 5)^{2} : 4 x^{4} + 20 x^{3} + 25 x^{2}

= \int 4 x^{4} + 20 x^{3} + 25 x^{2} 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 4 x^{4} d x + \int 20 x^{3} d x + \int 25 x^{2} d x

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

\int 20 x^{3} d x = 5 x^{4}

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

= \frac{4 x ^{5}}{5} + 5 x^{4} + \frac{25 x ^{3}}{3}

Add a constant to the solution

= \frac{4 x ^{5}}{5} + 5 x^{4} + \frac{25 x ^{3}}{3} + C

What is the integral of x^2(2x+5)^2 ?
The integral of x^2(2x+5)^2 is (4x^5)/5+5x^4+(25x^3)/3+C