Question

evaluate: integral from 3 to infinity: 1/(x-2)^(3/2) dx

Answer 1

\[ \huge \int_3^\infty (x-2)^{-\frac{3}{2}}dx \]

Answer 2

Maybe this form makes it a bit easier for you.

Answer 3

Can you do it step by step please

Answer 4

Maybe the term x-2 is confusing you, but you can always help yourself by using a simple substitution if this is the case.

\[ u=x-2 \rightarrow
\frac{du}{dx}=1 \\ \large \int_3^\infty \frac{du}{dx} u^{-\frac{3}{2}} dx = \int_3^\infty u^{-\frac{3}{2}}du\]

Answer 5

ok so far? this is a simple normal integral.

Answer 6

Yes continue

Answer 7

Rules of Integration

\[ \frac{-2}{\sqrt{u}} = \left. \frac{-2}{\sqrt{x-2}} \right|_3^\infty \]

Answer 8

Ok following

Answer 9

Now if you plug in \[x=\infty\] the term with the x in denominator will vanish, then you can plugin x=3 and you will get 2 as your solution.

Answer 10

Intergral of (x^4/(1+x^6))^2 dx over -1,inf