What is the integral of 8x^3-3/(2sqrt(x))+5 ?

The integral of 8x^3-3/(2sqrt(x))+5 is 2x^4-3sqrt(x)+5x+C

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integral of 8x^3-3/(2sqrt(x))+5

\int 8 x^{3} - \frac{3}{2 x} + 5 d x

2 x^{4} - 3 x + 5 x + C

Solution steps

\int 8 x^{3} - \frac{3}{2 x} + 5 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^{3} d x - \int \frac{3}{2 x} d x + \int 5 d x

\int 8 x^{3} d x = 2 x^{4}

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

\int 5 d x = 5 x

= 2 x^{4} - 3 x + 5 x

Add a constant to the solution

= 2 x^{4} - 3 x + 5 x + C

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What is the integral of 8x^3-3/(2sqrt(x))+5 ?
The integral of 8x^3-3/(2sqrt(x))+5 is 2x^4-3sqrt(x)+5x+C