What is the integral from 0 to 1 of (x^{-2}+3e^{3x}) ?

The integral from 0 to 1 of (x^{-2}+3e^{3x}) is diverges

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integral from 0 to 1 of (x^{-2}+3e^{3x})

\int_{0}^{1} (x^{- 2} + 3 e^{3 x}) d x

diverges

Solution steps

\int_{0}^{1} x^{- 2} + 3 e^{3 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} 3 e^{3 x} d x

\int_{0}^{1} x^{- 2} 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 (x^{-2}+3e^{3x}) ?
The integral from 0 to 1 of (x^{-2}+3e^{3x}) is diverges