What is the integral of (6-x^3)/(xsqrt(x)) ?

The integral of (6-x^3)/(xsqrt(x)) is -(12)/(sqrt(x))-2/5 x^{5/2}+C

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integral of (6-x^3)/(xsqrt(x))

\int \frac{6 - x ^{3}}{x x} d x

- \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int \frac{6 - x ^{3}}{x x} d x

Expand

\frac{6 - x ^{3}}{x x} : \frac{6}{x x} - x^{\frac{3}{2}}

= \int \frac{6}{x x} - x^{\frac{3}{2}} 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 \frac{6}{x x} d x - \int x^{\frac{3}{2}} d x

\int \frac{6}{x x} d x = - \frac{12}{x}

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

= - \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= - \frac{12}{x} - \frac{2}{5} x^{\frac{5}{2}} + C

What is the integral of (6-x^3)/(xsqrt(x)) ?
The integral of (6-x^3)/(xsqrt(x)) is -(12)/(sqrt(x))-2/5 x^{5/2}+C