What is the integral of (3/(x^3)-1/(\sqrt[3]{x)}) ?

The integral of (3/(x^3)-1/(\sqrt[3]{x)}) is -3/(2x^2)-3/2 x^{2/3}+C

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integral of (3/(x^3)-1/(\sqrt[3]{x)})

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

Solution steps

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

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

Add a constant to the solution

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

What is the integral of (3/(x^3)-1/(\sqrt[3]{x)}) ?
The integral of (3/(x^3)-1/(\sqrt[3]{x)}) is -3/(2x^2)-3/2 x^{2/3}+C