What is the integral from 0 to 1 of ((2x^2-5))/x ?

The integral from 0 to 1 of ((2x^2-5))/x is diverges

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integral from 0 to 1 of ((2x^2-5))/x

\int_{0}^{1} \frac{( 2 x ^{2} - 5 )}{x} d x

diverges

Solution steps

\int_{0}^{1} \frac{2 x ^{2} - 5}{x} d x

Expand

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

= \int_{0}^{1} 2 x - \frac{5}{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}^{1} 2 x d x - \int_{0}^{1} \frac{5}{x} d x

\int_{0}^{1} 2 x d x = 1

\int_{0}^{1} \frac{5}{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 1 of ((2x^2-5))/x ?
The integral from 0 to 1 of ((2x^2-5))/x is diverges