What is the integral from-1 to 2 of 4x^3+x^{-1} ?

The integral from-1 to 2 of 4x^3+x^{-1} is diverges

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integral from-1 to 2 of 4x^3+x^{-1}

\int_{- 1}^{2} 4 x^{3} + x^{- 1} d x

diverges

Solution steps

\int_{- 1}^{2} 4 x^{3} + x^{- 1} d x

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} 4 x^{3} + x^{- 1} d x + \int_{0}^{2} 4 x^{3} + x^{- 1} d x

\int_{- 1}^{0} 4 x^{3} + x^{- 1} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{0}^{36} \frac{9}{36 - x} d x

\int_{0}^{x} ln (1 - x) d x

\int_{0}^{10} 1.5 x d x

What is the integral from-1 to 2 of 4x^3+x^{-1} ?
The integral from-1 to 2 of 4x^3+x^{-1} is diverges