What is the integral from 0 to 4 of (4/x)-(4x) ?

The integral from 0 to 4 of (4/x)-(4x) is diverges

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integral from 0 to 4 of (4/x)-(4x)

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

diverges

Solution steps

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

\int_{0}^{4} \frac{4}{x} 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 4 of (4/x)-(4x) ?
The integral from 0 to 4 of (4/x)-(4x) is diverges