Need to find integral [1, 5e] [1/t] dt

[hank]

Here's the problem:

\(\displaystyle \L \int_1^{5e}\, \left[\frac{1}{t}\right]\,dt\)

Here's the answer I get:

ln5e - ln1

But apparently, this isn't correct. The answer I was given was 1 + ln5. Not sure how they got that, could someone fill me in?

 

[mammothrob]

your answer is right, they just simplified it.

ln(5e)-ln(1)=

ln(5) + ln(e) - ln(1)=

ln(5) + 1 + 0=

1 + ln(5) <------ your books answer


Property: ln(ab)=ln(a) + ln(b) & ln(e)= 1

 

[royhaas]

Since ln1=0 and ln5e=ln5+lne=ln5+1, you just needed to simplify.

 

[hank]

Oh, I see now. The 5e is what confused me. I knew about breaking up logs, but it didn't occur to me that you could do that when you have the log of two constants multiplied together.

Thanks!