Question

elavualte indefinite integrals

1/x^(1/2) cos.( t^1/2 +3) dx

Answer 1

\[\huge \int\limits \frac{1}{x^{1/2}}\cdot \cos(t^{1/2}+3) \; dx\]Like this? Is that t suppose to be an x by chance?

Answer 2

yes, sorry. that is one t^1/2 not x^1/2

Answer 3

*that one is

Answer 4

\[\large \int\limits\limits \frac{1}{t^{1/2}}\cdot \cos(t^{1/2}+3) \; dt\]
Oh ok :)
Hmm looks like you can do a nice U-substitution for this one.

Answer 5

okay,

Answer 6

So with a U-sub, we're trying to find a U and U' somewhere in the problem.

If you look at the inside of the cosine, taking the derivative of that should give you something similar to the other term.

So try letting,\[\large u=t^{1/2}+3\]And see if you can match up your dU from there.

Answer 7

Were you able to get a dU? Or confused? :)

Answer 8

kind of confused

Answer 9

but trying to figure it out

Answer 10

We're trying to do something like this,
Simplify the integral so it's very easy to integrate.
We just have to figure out what DU is so we can make sure we didn't miss anything.