What is the integral of xsqrt(x^2)+1 ?

The integral of xsqrt(x^2)+1 is (x^3)/3+x+C

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integral of xsqrt(x^2)+1

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

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

Solution steps

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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What is the integral of xsqrt(x^2)+1 ?
The integral of xsqrt(x^2)+1 is (x^3)/3+x+C