What is the integral from 1 to infinity of x^{-3} ?

The integral from 1 to infinity of x^{-3} is 1/2

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integral from 1 to infinity of x^{-3}

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{2}

y^{^{'}} - 5 y = 4 e^{7 t}

x \to 0 lim (x^{2} + a x + 2)

2 t^{2} - 3 t - 1

\int \frac{1}{4 x ^{2} - 81} d x

\int \frac{x ^{3}}{25 + x ^{8}} d x

What is the integral from 1 to infinity of x^{-3} ?
The integral from 1 to infinity of x^{-3} is 1/2