Thread: Integration - exponents and logs

1. Integration - exponents and logs

Hey again,
Looks like integration by parts is real trouble for me

I have a problem that I must integrate:

$\displaystyle \int{s2^s}ds$

I set:

$\displaystyle u=s$

$\displaystyle dv=2^s$

$\displaystyle du=1$

$\displaystyle v=\frac{2^s}{\ln{2}}$

And I get:

$\displaystyle s\ln{2}-\int{\frac{2^s}{\ln{2}}}$

I have no idea what to do with that integral

2. Originally Posted by Coco87
Hey again,
Looks like integration by parts is real trouble for me

I have a problem that I must integrate:

$\displaystyle \int{s2^s}ds$

I set:

$\displaystyle u=s$

$\displaystyle dv=2^s$

$\displaystyle du=1$

$\displaystyle v=\frac{2^s}{\ln{2}}$

And I get:

$\displaystyle s\ln{2}-\int{\frac{2^s}{\ln{2}}}$

I have no idea what to do with that integral
But...didn't you just integrate it? Don't let the ln2 confuse you, it's just a constant, you can pull it out like this.

$\displaystyle \frac{1}{\ln{2}} \int 2^s ds$

3. Originally Posted by Chop Suey
But...didn't you just integrate it? Don't let the ln2 confuse you, it's just a constant, you can pull it out like this.

$\displaystyle \frac{1}{\ln{2}} \int 2^s ds$
... that was the issue... got the correct answer.

Thanks!

I never thought of $\displaystyle \ln{}$ as a constant, you have just saved me a headache on previous and future problems