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

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

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integral from 1 to infinity of (1/(x^3))

\int_{1}^{\infty} (\frac{1}{x ^{3}}) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{3}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

l a pl a ce t r an s f or m 4 t^{2} cos (2 t) + 5 t e^{- 7 t}

\frac{d}{d x} (4 x^{9} + 2 x^{5})

d er i v a t i v e f (x) = \frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}}

f^{^{'}} (t) - f (t) = 6 t

y^{2} + x^{2} y^{^{'}} = x y y^{^{'}}

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