What is the integral from-9 to-2 of-3/((x+3)^2) ?

The integral from-9 to-2 of-3/((x+3)^2) is diverges

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integral from-9 to-2 of-3/((x+3)^2)

\int_{- 9}^{- 2} - \frac{3}{( x + 3 ) ^{2}} d x

diverges

Solution steps

\int_{- 9}^{- 2} - \frac{3}{( x + 3 ) ^{2}} d x

Find undefined (singularity) points:

x = - 3

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_{- 9}^{- 3} - \frac{3}{( x + 3 ) ^{2}} d x + \int_{- 3}^{- 2} - \frac{3}{( x + 3 ) ^{2}} d x

\int_{- 9}^{- 3} - \frac{3}{( x + 3 ) ^{2}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{2} 9 d x

\int_{0}^{\frac{π}{3}} sec (θ) d θ

\int_{- 1}^{2} \frac{1}{x ^{2} - 4} d x

\int_{1}^{x^{4}} sec (x) d x

\int_{0}^{x} \frac{1}{1 - t ^{2}} d t

What is the integral from-9 to-2 of-3/((x+3)^2) ?
The integral from-9 to-2 of-3/((x+3)^2) is diverges