What is the integral of sqrt(x)(x-4) ?

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

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integral of sqrt(x)(x-4)

\int x (x - 4) d x

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

Solution steps

\int x (x - 4) d x

Expand

x (x - 4) : x^{\frac{3}{2}} - 4 x

= \int x^{\frac{3}{2}} - 4 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 x^{\frac{3}{2}} d x - \int 4 x d x

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

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

= \frac{2}{5} x^{\frac{5}{2}} - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - \frac{8}{3} x^{\frac{3}{2}} + C

\int (\frac{2 x ^{2} + 4 x - 3}{x ^{2}}) d x

\int x 3 x^{2} + 5 d x

\int x^{2} 4 + x d x

\int \frac{1}{9 - x ^{4}} d x

\int x^{3} x^{2} + 14 d x

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