What is the integral from-4 to 1 of 1/(x^4) ?

The integral from-4 to 1 of 1/(x^4) is diverges

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integral from-4 to 1 of 1/(x^4)

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = 0

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_{- 4}^{0} \frac{1}{x ^{4}} d x + \int_{0}^{1} \frac{1}{x ^{4}} d x

\int_{- 4}^{0} \frac{1}{x ^{4}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{- 2}^{- 1} (4 y^{3} + \frac{2}{y ^{3}}) d y

4 t^{4}

\frac{d}{d x} (\frac{x ^{n}}{( 1 + x ) ^{n}})

\frac{d}{d x} (ln (x) - x)

\int - 2 sin (x) - 10 cos (x) d x

What is the integral from-4 to 1 of 1/(x^4) ?
The integral from-4 to 1 of 1/(x^4) is diverges