What is the integral from-2 to 1 of 1/((1+5x)^3) ?

The integral from-2 to 1 of 1/((1+5x)^3) is diverges

integral from-2 to 1 of 1/((1+5x)^3)

\int_{- 2}^{1} \frac{1}{( 1 + 5 x ) ^{3}} d x

diverges

Solution steps

\int_{- 2}^{1} \frac{1}{( 1 + 5 x ) ^{3}} d x

Find undefined (singularity) points:

x = - \frac{1}{5}

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_{- 2}^{- \frac{1}{5}} \frac{1}{( 1 + 5 x ) ^{3}} d x + \int_{- \frac{1}{5}}^{1} \frac{1}{( 1 + 5 x ) ^{3}} d x

\int_{- 2}^{- \frac{1}{5}} \frac{1}{( 1 + 5 x ) ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{4} (x - 1)^{2} d x

\int_{1}^{3} - x + 4 d x

\int_{0}^{0.8} x \cdot e^{x} d x

\int_{1}^{4} \frac{5 e ^{- x}}{2} d x

\int_{x}^{0} e^{- 3 t} d t

What is the integral from-2 to 1 of 1/((1+5x)^3) ?
The integral from-2 to 1 of 1/((1+5x)^3) is diverges