What is the integral from 0 to 3 of (4x^3+2/(x^3)) ?

The integral from 0 to 3 of (4x^3+2/(x^3)) is diverges

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integral from 0 to 3 of (4x^3+2/(x^3))

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

diverges

Solution steps

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

\int_{0}^{3} 4 x^{3} d x = 81

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from 0 to 3 of (4x^3+2/(x^3)) ?
The integral from 0 to 3 of (4x^3+2/(x^3)) is diverges