What is the integral of (7x^2-5)^2 ?

The integral of (7x^2-5)^2 is (49x^5)/5-(70x^3)/3+25x+C

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integral of (7x^2-5)^2

\int (7 x^{2} - 5)^{2} d x

\frac{49 x ^{5}}{5} - \frac{70 x ^{3}}{3} + 25 x + C

Solution steps

\int (7 x^{2} - 5)^{2} d x

Expand

(7 x^{2} - 5)^{2} : 49 x^{4} - 70 x^{2} + 25

= \int 49 x^{4} - 70 x^{2} + 25 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^{4} d x - \int 70 x^{2} d x + \int 25 d x

\int 49 x^{4} d x = \frac{49 x ^{5}}{5}

\int 70 x^{2} d x = \frac{70 x ^{3}}{3}

\int 25 d x = 25 x

= \frac{49 x ^{5}}{5} - \frac{70 x ^{3}}{3} + 25 x

Add a constant to the solution

= \frac{49 x ^{5}}{5} - \frac{70 x ^{3}}{3} + 25 x + C

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What is the integral of (7x^2-5)^2 ?
The integral of (7x^2-5)^2 is (49x^5)/5-(70x^3)/3+25x+C