What is the integral from 0 to 1 of ((x^3+2x^2+5)/x) ?

The integral from 0 to 1 of ((x^3+2x^2+5)/x) is diverges

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integral from 0 to 1 of ((x^3+2x^2+5)/x)

\int_{0}^{1} (\frac{x ^{3} + 2 x ^{2} + 5}{x}) d x

diverges

Solution steps

\int_{0}^{1} \frac{x ^{3} + 2 x ^{2} + 5}{x} d x

Expand

\frac{x ^{3} + 2 x ^{2} + 5}{x} : x^{2} + 2 x + \frac{5}{x}

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\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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\int_{0}^{1} π (1 - y) d y

What is the integral from 0 to 1 of ((x^3+2x^2+5)/x) ?
The integral from 0 to 1 of ((x^3+2x^2+5)/x) is diverges