What is the integral of (x^2+x-6) ?

The integral of (x^2+x-6) is (x^3)/3+(x^2)/2-6x+C

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integral of (x^2+x-6)

\int (x^{2} + x - 6) d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + C

Solution steps

\int x^{2} + x - 6 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 x d x - \int 6 d x

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

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

\int 6 d x = 6 x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x + C

\int \frac{x}{25 + 4 x ^{2}} d x

\frac{d}{d t} (\frac{k}{t})

\frac{d}{d x} (e^{x y} (y + x \frac{d y}{d x}))

\int \frac{6}{x ln ( x )} d x

What is the integral of (x^2+x-6) ?
The integral of (x^2+x-6) is (x^3)/3+(x^2)/2-6x+C