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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = - 1

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_{- 2}^{- 1} \frac{1}{( x + 1 ) ^{3}} d x + \int_{- 1}^{3} \frac{1}{( x + 1 ) ^{3}} d x

\int_{- 2}^{- 1} \frac{1}{( x + 1 ) ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{2}^{10} x d x

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

\int_{0}^{7} e^{x - 7} d x

\int_{x}^{y} e^{- t^{2}} d t

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

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