What is the integral of 2x^3-2x^2+2x-10 ?

The integral of 2x^3-2x^2+2x-10 is (x^4)/2-(2x^3)/3+x^2-10x+C

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integral of 2x^3-2x^2+2x-10

\int 2 x^{3} - 2 x^{2} + 2 x - 10 d x

\frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} + x^{2} - 10 x + C

Solution steps

\int 2 x^{3} - 2 x^{2} + 2 x - 10 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^{3} d x - \int 2 x^{2} d x + \int 2 x d x - \int 10 d x

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

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

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

\int 10 d x = 10 x

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} + x^{2} - 10 x

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} + x^{2} - 10 x + C

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What is the integral of 2x^3-2x^2+2x-10 ?
The integral of 2x^3-2x^2+2x-10 is (x^4)/2-(2x^3)/3+x^2-10x+C