# How can you use the tabular method to integrate xcos(x^2)

1. Aug 2, 2017

### lioric

1. The problem statement, all variables and given/known data
This is not a homework but since asked me I'm posting it here. I know how to intergrate by parts and can do this using formula
But I'd like to do this using the tabular method

Question
Integrate xcos(x^2) using tabular method

2. Relevant equations
The table with derivative on one volume and integral on the other column

3. The attempt at a solution
I know we can differentiate the one which is harder to intergrate so I integrated the x and differentiated cos(x^2)

So I get -2sin(x^2) for the derivative column and (x^2)/2 on the intergral side
When I multiply the results as said in tabular method and integrate the last portion, I get

(X^2)/2 * cos(x^2) -2 integrated by sin(x^2) * (x^2)/2

Last edited by a moderator: Aug 2, 2017
2. Aug 2, 2017

### NFuller

The tabular method is integration by parts. It is just organizing the steps into a table. If you understand the formula than there is no need to make a table.
The first derivative is $-2x\text{sin}(x^{2})$ not $-2\text{sin}(x^{2})$. I don't think this is a good method to solve this problem though. This integral is relatively trivial using the u-substitution $u=x^{2}$.