What is the integral of 4/(x^3)-5xsqrt(x) ?

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

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integral of 4/(x^3)-5xsqrt(x)

\int \frac{4}{x ^{3}} - 5 x x d x

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

Solution steps

\int \frac{4}{x ^{3}} - 5 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 \frac{4}{x ^{3}} d x - \int 5 x x d x

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

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

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

Add a constant to the solution

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

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