What is the integral of x^2(7+x)^2 ?

The integral of x^2(7+x)^2 is (49x^3)/3+(7x^4)/2+(x^5)/5+C

integral of x^2(7+x)^2

\int x^{2} (7 + x)^{2} d x

\frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5} + C

Solution steps

\int x^{2} (7 + x)^{2} d x

Expand

x^{2} (7 + x)^{2} : 49 x^{2} + 14 x^{3} + x^{4}

= \int 49 x^{2} + 14 x^{3} + x^{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 49 x^{2} d x + \int 14 x^{3} d x + \int x^{4} d x

\int 49 x^{2} d x = \frac{49 x ^{3}}{3}

\int 14 x^{3} d x = \frac{7 x ^{4}}{2}

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

= \frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5} + C

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What is the integral of x^2(7+x)^2 ?
The integral of x^2(7+x)^2 is (49x^3)/3+(7x^4)/2+(x^5)/5+C