Question

[Calculus 2] Solve the integral (question in comments).

Answer 1

If someone could explain how to solve this for me, it would be great! :)

Answer 2

that looks like a doozie

Answer 3

hmm\[\int2^{-(x^{-1})}x^{-2}~dx\]

Answer 4

might be a by parts using the base as your downer and the x^-2 as the upper

Answer 5

what is the derivative of 2^-(1/x) ?

Answer 6

It's not integration by parts- this is from test 1. We did by parts on test 2.

Answer 7

in general
\[Dx~[a^x]=a^xlna\]

this might be an ugly looking ...reverse product rule

Answer 8

2^-(1/x) = y

ln(2^-(1/x)) = ln(y)

-1/x ln(2) = ln(y)

ln(2)/x^2 = y'/y

ln(2) y/x^2 = y'

ln(2) 2^-(1/x)/x^2 = y'

all we are missing is a useful ln2

Answer 9

\[\frac1{ln2}\int ln(2)\frac{2^{-1/x}}{x^2}dx=\frac1{ln2}~2^{-1/x}\]

Answer 10

+C

Answer 11

i spose youd refer to it as a u-sub?

Answer 12

^Yeah, it looks more like that than anything else.

Answer 13

Thanks for your help! :)