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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

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

\int_{- 1}^{- \frac{2}{3}} \frac{1}{( 2 + 3 x ) ^{3}} 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 2 of 1/((2+3x)^3) ?
The integral from-1 to 2 of 1/((2+3x)^3) is diverges