What is the integral of (7x^3-5)^2 ?

The integral of (7x^3-5)^2 is 7x^7-(35x^4)/2+25x+C

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integral of (7x^3-5)^2

\int (7 x^{3} - 5)^{2} d x

7 x^{7} - \frac{35 x ^{4}}{2} + 25 x + C

Solution steps

\int (7 x^{3} - 5)^{2} d x

Expand

(7 x^{3} - 5)^{2} : 49 x^{6} - 70 x^{3} + 25

= \int 49 x^{6} - 70 x^{3} + 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^{6} d x - \int 70 x^{3} d x + \int 25 d x

\int 49 x^{6} d x = 7 x^{7}

\int 70 x^{3} d x = \frac{35 x ^{4}}{2}

\int 25 d x = 25 x

= 7 x^{7} - \frac{35 x ^{4}}{2} + 25 x

Add a constant to the solution

= 7 x^{7} - \frac{35 x ^{4}}{2} + 25 x + C

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What is the integral of (7x^3-5)^2 ?
The integral of (7x^3-5)^2 is 7x^7-(35x^4)/2+25x+C