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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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