What is the integral from 1 to infinity of x^{-5/4} ?

The integral from 1 to infinity of x^{-5/4} is 4

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integral from 1 to infinity of x^{-5/4}

\int_{1}^{\infty} x^{- \frac{5}{4}} d x

4

Solution steps

\int_{1}^{\infty} x^{- \frac{5}{4}} d x

Compute the indefinite integral:

\int x^{- \frac{5}{4}} d x = - \frac{4}{x ^{\frac{1}{4}}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- \frac{5}{4}} d x = 0 - (- 4)

= 0 - (- 4)

Simplify

= 4

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

e^{- 2 t} cos^{2} (t)

What is the integral from 1 to infinity of x^{-5/4} ?
The integral from 1 to infinity of x^{-5/4} is 4