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Popular >

integral of (8+x)(2x-8)

Solution

\int (8 + x) (2 x - 8) d x

Solution

\frac{2 x ^{3}}{3} + 4 x^{2} - 64 x + C

Solution steps

\int (8 + x) (2 x - 8) d x

Expand

(8 + x) (2 x - 8) : 2 x^{2} + 8 x - 64

= \int 2 x^{2} + 8 x - 64 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 2 x^{2} d x + \int 8 x d x - \int 64 d x

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

\int 8 x d x = 4 x^{2}

\int 64 d x = 64 x

= \frac{2 x ^{3}}{3} + 4 x^{2} - 64 x

Add a constant to the solution

= \frac{2 x ^{3}}{3} + 4 x^{2} - 64 x + C

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Frequently Asked Questions (FAQ)

What is the integral of (8+x)(2x-8) ?
The integral of (8+x)(2x-8) is (2x^3)/3+4x^2-64x+C