How can I solve this U-Substitution problem involving cos and square roots?

[01010011]

Hi,
For this integration by substitution problem, I am not sure whether I should:

1. simplify the problem first, then select U, find the derivative of U, then integrate

or

2. use the product rule first (on the upper part of the equation), then select U, then find the derivative of U, then integrate,

or

3. if I could just cancel like terms first, and be left with cos to integrate

Homework Statement

Evaluate the indefinite integral

Homework Equations

integral of cos * (square root of t) / (square root of t) dt

The Attempt at a Solution

integral of cos * (square root of t) / (square root of t) dt

integral of [cos t^(1/2)] / t^(1/2) dt

let U = cos t ^ 1/2

du = 1/2 (sin t 3/2) / (t 3/2)

Now I am really lost! What should I do?

 

[Count Iblis]

Try t = x^2

 

[01010011]

Try t = x^2

Thanks for your reply Count Iblis. How does x come in this?

 

[Lunat1c]

It's just a variable name. If you prefer to use 'u' instead, make it t = u^2.

 

[01010011]

Still trying to figure out what you mean by t = u^2.

Up to where was I right?

 

[Lunat1c]

t = u^2 means you're going to use the substitution u = sqrt(t) to evaluate your integral. I'm pretty sure you can continue from there