Integration with hyp trig (1 Viewer)

[Engen]

Hi

Sorry i dont know latex but the question is this:

int 1/sqrt((x+2)^2 + 9) dx

I know that it should come out in the form ln|f(x) + sqrt([f(x)]^2 + a^2)| + C but not having the answers is a pain and wolfram gives me a hyperbolic trig function however the step before it turns into hyp trig it's in ln form as stated but it multiplies everything on the inside of the log by 1/3.

Could somebody explain to me how they pull a 1/3 out or where it comes from?

Wolfram link HERE

 

[asianese]

Remember that log(1/3) is just a constant so you can ignore it - it gets mumbled within the +C

 

[Aesytic]

also, if wolframalpha doesn't give you the answer you're looking for, you can also get it to differentiate your answer, and it should come up with the original function

 

[Engen]

I'm talking about this:



How does it become a constant if it's inside the log?

 

[deswa1]

log(AB)=logA+logB -> when integrating functions that give you a log, you can therefore put the constant inside the logarithm. This makes things like some mechanics questions easier.

 

[Engen]

I see.

Thanks everyone for their input.

Have a great day.