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

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

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integral of xsqrt(x^2)+2

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

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

Solution steps

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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