What is the integral from-8 to-6 of 6/((x+7)^4) ?

The integral from-8 to-6 of 6/((x+7)^4) is diverges

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integral from-8 to-6 of 6/((x+7)^4)

\int_{- 8}^{- 6} \frac{6}{( x + 7 ) ^{4}} d x

diverges

Solution steps

\int_{- 8}^{- 6} \frac{6}{( x + 7 ) ^{4}} d x

Find undefined (singularity) points:

x = - 7

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_{- 8}^{- 7} \frac{6}{( x + 7 ) ^{4}} d x + \int_{- 7}^{- 6} \frac{6}{( x + 7 ) ^{4}} d x

\int_{- 8}^{- 7} \frac{6}{( x + 7 ) ^{4}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from-8 to-6 of 6/((x+7)^4) ?
The integral from-8 to-6 of 6/((x+7)^4) is diverges