Thread: Simple Integration

I have an integrating factor of and have simplified it to near the end of the problem we are required to integrate which comes to right?

Now my friend has kept the integrating factor in the form throughout the problem and thus has to integrate at the end of the problem. She, however, thinks that this becomes .

Obviosuly one of us is wrong; but who?

Originally Posted by AmberLamps

I have an integrating factor of and have simplified it to near the end of the problem we are required to integrate which comes to right?

Now my friend has kept the integrating factor in the form throughout the problem and thus has to integrate at the end of the problem. She, however, thinks that this becomes .

Obviosuly one of us is wrong; but who?

If you post the problem, I could tell you for sure, but given an integrating factor of , I would simplify this to . The log and the exponential then cancel out to give you an integrating factor of . Is this the integrating factor that you actually got?

Secondly, how did your friend get ? Anycase, he is wrong, if you take the super complicated and long way around, you still get the integration of .

Out of interest, if you want to do the long way, let u = ln(t), hence t = exp(u) then let v =4u. Don't for get to change the dt in each case.