What is the integral from 2 to infinity of 8/(x^3) ?

The integral from 2 to infinity of 8/(x^3) is 1

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integral from 2 to infinity of 8/(x^3)

\int_{2}^{\infty} \frac{8}{x ^{3}} d x

1

Solution steps

\int_{2}^{\infty} \frac{8}{x ^{3}} d x

Compute the indefinite integral:

\int \frac{8}{x ^{3}} d x = - \frac{4}{x ^{2}} + C

Compute the boundaries:

\int_{2}^{\infty} \frac{8}{x ^{3}} d x = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

\frac{1}{x - 1}

\int \frac{10}{x} + \frac{2}{x ^{2}} + \frac{7}{x ^{3}} d x

\int 1 + \frac{1}{4 x} d x

\frac{d}{d x} (cot (3 x^{4} - 2 x^{3} - 3))

x \to 4 lim (\frac{6 x - 1}{2 x - 9})

What is the integral from 2 to infinity of 8/(x^3) ?
The integral from 2 to infinity of 8/(x^3) is 1