What is the integral of (14x-8)(7x^2-8x+3)^2 ?

The integral of (14x-8)(7x^2-8x+3)^2 is (343x^6)/3-392x^5+595x^4-(1520x^3)/3+255x^2-72x+C

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integral of (14x-8)(7x^2-8x+3)^2

\int (14 x - 8) (7 x^{2} - 8 x + 3)^{2} d x

\frac{343 x ^{6}}{3} - 392 x^{5} + 595 x^{4} - \frac{1520 x ^{3}}{3} + 255 x^{2} - 72 x + C

Solution steps

\int (14 x - 8) (7 x^{2} - 8 x + 3)^{2} d x

Expand

(14 x - 8) (7 x^{2} - 8 x + 3)^{2} : 686 x^{5} - 1960 x^{4} + 2380 x^{3} - 1520 x^{2} + 510 x - 72

= \int 686 x^{5} - 1960 x^{4} + 2380 x^{3} - 1520 x^{2} + 510 x - 72 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 686 x^{5} d x - \int 1960 x^{4} d x + \int 2380 x^{3} d x - \int 1520 x^{2} d x + \int 510 x d x - \int 72 d x

\int 686 x^{5} d x = \frac{343 x ^{6}}{3}

\int 1960 x^{4} d x = 392 x^{5}

\int 2380 x^{3} d x = 595 x^{4}

\int 1520 x^{2} d x = \frac{1520 x ^{3}}{3}

\int 510 x d x = 255 x^{2}

\int 72 d x = 72 x

= \frac{343 x ^{6}}{3} - 392 x^{5} + 595 x^{4} - \frac{1520 x ^{3}}{3} + 255 x^{2} - 72 x

Add a constant to the solution

= \frac{343 x ^{6}}{3} - 392 x^{5} + 595 x^{4} - \frac{1520 x ^{3}}{3} + 255 x^{2} - 72 x + C

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What is the integral of (14x-8)(7x^2-8x+3)^2 ?
The integral of (14x-8)(7x^2-8x+3)^2 is (343x^6)/3-392x^5+595x^4-(1520x^3)/3+255x^2-72x+C