integrate dx/[(sqrt(x))(3^(sqrt(x))]

Question

anonymous · Answer

I put u=sqrt(x)

hartnn · Answer

put u= sqrt x
du=.. ?

anonymous · Answer

2du=1/sqrt(x)dx

anonymous · Answer

think i'm stuck where i need to use a log property..

hartnn · Answer

oh, you don't need to,
don't you know the standard formula for $\int a^xdx=... ?$

anonymous · Answer

wouldn't I have 3^(-u) at one point though?

hartnn · Answer

yes, so you can use the formula for integral of a^x dx, right ?

hartnn · Answer

$2\int 3^{-u}du = 2[\dfrac{3^{-u}}{(-1)\log u}]+c $

anonymous · Answer

we can also do it by substituting 3^ sqrt(x) as t

anonymous · Answer

where did the log come from? what am i forgetting?

hartnn · Answer

$\int a^xdx=a^x/ \log a +c$

anonymous · Answer

ahhh, yep. that was it. thanks man

hartnn · Answer

sorry, typo,
$2\int 3^{-u}du = 2[\dfrac{3^{-u}}{(-1)\log 3}]+c$

anonymous · Answer

where is the (-1) coming from?

hartnn · Answer

in derivatives, we multiply by the co-efficient of variable, 
similarly, in integration, we divide by the co-efficient of variable.
so, here its -u thats why we need to divide by -1

anonymous · Answer

ahhh, ok. good explanation, thanks.

hartnn · Answer

welcome ^_^