What is the integral of sqrt(x)(5x-3) ?

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

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integral of sqrt(x)(5x-3)

\int x (5 x - 3) d x

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

Solution steps

\int x (5 x - 3) d x

Expand

x (5 x - 3) : 5 x^{\frac{3}{2}} - 3 x

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

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

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

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

Add a constant to the solution

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

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