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

The integral of (2x^2+7)^2 is (4x^5)/5+(28x^3)/3+49x+C

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

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

\frac{4 x ^{5}}{5} + \frac{28 x ^{3}}{3} + 49 x + C

Solution steps

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

Expand

(2 x^{2} + 7)^{2} : 4 x^{4} + 28 x^{2} + 49

= \int 4 x^{4} + 28 x^{2} + 49 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 28 x^{2} d x + \int 49 d x

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

\int 28 x^{2} d x = \frac{28 x ^{3}}{3}

\int 49 d x = 49 x

= \frac{4 x ^{5}}{5} + \frac{28 x ^{3}}{3} + 49 x

Add a constant to the solution

= \frac{4 x ^{5}}{5} + \frac{28 x ^{3}}{3} + 49 x + C

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What is the integral of (2x^2+7)^2 ?
The integral of (2x^2+7)^2 is (4x^5)/5+(28x^3)/3+49x+C