What is the integral from 1 to infinity of x^{-5/2} ?

The integral from 1 to infinity of x^{-5/2} is 2/3

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integral from 1 to infinity of x^{-5/2}

\int_{1}^{\infty} x^{- \frac{5}{2}} d x

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{1}^{\infty} x^{- \frac{5}{2}} d x

Compute the indefinite integral:

\int x^{- \frac{5}{2}} d x = - \frac{2}{3 x ^{\frac{3}{2}}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- \frac{5}{2}} d x = 0 - (- \frac{2}{3})

= 0 - (- \frac{2}{3})

Simplify

= \frac{2}{3}

\frac{\partial}{\partial x} ((2 x - 2)^{4} (x^{2} + x + 1)^{5})

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

4 e^{- 7 t} \cdot cos (9 t)

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

\int 1 - e^{- x^{2}} d x

What is the integral from 1 to infinity of x^{-5/2} ?
The integral from 1 to infinity of x^{-5/2} is 2/3