What is the integral from 0 to 2 of (4/(sqrt(x^3))-(10)/(\sqrt[3]{x^2)}) ?

The integral from 0 to 2 of (4/(sqrt(x^3))-(10)/(\sqrt[3]{x^2)}) is diverges

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integral from 0 to 2 of (4/(sqrt(x^3))-(10)/(\sqrt[3]{x^2)})

\int_{0}^{2} (\frac{4}{x ^{3}} - \frac{10}{3 x ^{2}}) d x

diverges

Solution steps

\int_{0}^{2} \frac{4}{x ^{3}} - \frac{10}{3 x ^{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_{0}^{2} \frac{4}{x ^{3}} d x - \int_{0}^{2} \frac{10}{3 x ^{2}} d x

\int_{0}^{2} \frac{4}{x ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{2}^{3} \frac{1}{x ^{3}} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin (θ) d θ

\int_{2}^{3} \frac{1}{( x - 1 ) ^{3}} d x

What is the integral from 0 to 2 of (4/(sqrt(x^3))-(10)/(\sqrt[3]{x^2)}) ?
The integral from 0 to 2 of (4/(sqrt(x^3))-(10)/(\sqrt[3]{x^2)}) is diverges