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

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

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

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

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + C

Solution steps

\int x^{2} + 2 x - 7 x d x

Simplify

= \int x^{2} - 5 x 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 x^{2} d x - \int 5 x d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + C

\int \frac{5}{5 x} d x

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