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

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

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integral of (x^2+x-2)

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{d}{d x} (arctan (\frac{1}{2} x))

f (x) = 7 - 2 x^{2}

\int \frac{x + 3}{x ^{2} + 1} d x

\frac{d y}{d x} - \frac{2}{x} y = x^{2} - 1

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