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

\int sec (32 w) tan (32 w) d w

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\int \frac{1}{( 2 x ) ^{2}} d x

\int \frac{x ^{2} - 1}{x ^{2}} d x

\int - \frac{1}{3 y} d y

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