Need a Few Hints for Substitution

[whatisphysics]

I've been doing Calculus examples using substitution recently, and some are very easy to spot when to make what u, but sometimes it's not that easy. I'm having trouble determining which equations I should make as u, and which ones I shouldn't.

I would greatly appreciate it if I could be given some hints for these problems!

Thanks in advance!

 

[iamalexalright]

Well, a thing I always try is to pick a part of the integral, take the derivative of that and see if that will help me simply.

So for the first one I would look at the derivative of:
u = x
u = ln(2x)

Take derivatives of both of those and see if using one of them you can simplify the integral (hint - one of them simplifies it and the other doesnt!)
The second one is a little trickier: probably have to use a trig substitution

The third one: can you do this integral:
\int \frac{4dt}{t^{7}}

Fourth: similar in idea of picking a good u as the third problem. Look at that one first and see if you can come up with anything (hint, look at the exponents of the e's)

 

[whatisphysics]

Well, a thing I always try is to pick a part of the integral, take the derivative of that and see if that will help me simply.

So for the first one I would look at the derivative of:
u = x
u = ln(2x)

Take derivatives of both of those and see if using one of them you can simplify the integral (hint - one of them simplifies it and the other doesnt!)



The second one is a little trickier: probably have to use a trig substitution

The third one: can you do this integral:
\int \frac{4dt}{t^{7}}

Fourth: similar in idea of picking a good u as the third problem. Look at that one first and see if you can come up with anything (hint, look at the exponents of the e's)

Thanks! Gonna jump into these questions right now!

 

[whatisphysics]

Well, a thing I always try is to pick a part of the integral, take the derivative of that and see if that will help me simply.

So for the first one I would look at the derivative of:
u = x
u = ln(2x)

Does this look okay?

 

[Dick]

That's a good start. But if u=log(2x), du isn't quite dx/(2x). Can you try that one again. Use the chain rule.

 

[HallsofIvy]

Or use the fact that ln(2x)= ln(x)+ ln(2).

 

[whatisphysics]

Okay, thanks for all the input. Will try them again tomorrow morning. Need to get some rest! I'm sure I will dream about cal tonight...