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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = - 2

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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

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

\int_{0}^{3} k x^{2} + \frac{1}{30} d x

\int_{\frac{y}{2}}^{\frac{1}{2}} e^{- x^{2}} d x

\int_{0}^{π} cos^{7} (x) d x

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