What is the integral of 5x^2+sqrt(x) ?

The integral of 5x^2+sqrt(x) is (5x^3)/3+2/3 x^{3/2}+C

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integral of 5x^2+sqrt(x)

\int 5 x^{2} + x d x

\frac{5 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 5 x^{2} + x 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 5 x^{2} d x + \int x d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

= \frac{5 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{5 x ^{3}}{3} + \frac{2}{3} x^{\frac{3}{2}} + C

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What is the integral of 5x^2+sqrt(x) ?
The integral of 5x^2+sqrt(x) is (5x^3)/3+2/3 x^{3/2}+C