What is the integral of (8x+sqrt(x)) ?

The integral of (8x+sqrt(x)) is 4x^2+2/3 x^{3/2}+C

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integral of (8x+sqrt(x))

\int (8 x + x) d x

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

Solution steps

\int 8 x + 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 8 x d x + \int x d x

\int 8 x d x = 4 x^{2}

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

= 4 x^{2} + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 4 x^{2} + \frac{2}{3} x^{\frac{3}{2}} + C

What is the integral of (8x+sqrt(x)) ?
The integral of (8x+sqrt(x)) is 4x^2+2/3 x^{3/2}+C