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

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

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

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

diverges

Solution steps

\int_{- 2}^{1} \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}^{1} \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

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\int_{0}^{π} 2 + cos^{2} (t) d t

\int_{- 2}^{1} (6 - x^{2}) - (x + 4) d x

\int_{x}^{1} (y - 1)^{2} d y

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