# U-Substitution involving cos

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?

## Answers and Replies

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