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

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

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

\int_{1}^{\infty} x^{- \frac{3}{2}} d x

2

Solution steps

\int_{1}^{\infty} x^{- \frac{3}{2}} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 2)

Simplify

= 2

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\frac{\partial}{\partial x} (sec^{2} (x) - 1)

\int (1 + cos (x))^{2} sin (x) d x

f (x) = 7 (x^{3} - x)^{4}

t^{2} e^{- 2 t} sin (3 t + 30)

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