What is the integral from 1 to infinity of x^{-4} ?

The integral from 1 to infinity of x^{-4} is 1/3

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integral from 1 to infinity of x^{-4}

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

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

Compute the indefinite integral:

\int x^{- 4} d x = - \frac{1}{3 x ^{3}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- 4} d x = 0 - (- \frac{1}{3})

= 0 - (- \frac{1}{3})

Simplify

= \frac{1}{3}

x \to 0 lim (\frac{3 - 3 e ^{- x}}{e ^{x} - 1})

6 x^{5} + 4 e^{x}

x^{3} + y^{3} = 1

\int \frac{9 x ^{2}}{x ^{2} - 4} d x

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

What is the integral from 1 to infinity of x^{-4} ?
The integral from 1 to infinity of x^{-4} is 1/3