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# Integrate x(1+cosx)

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1. Hi I've tried many times to integrate x(1+cosx) but I keep getting xsinx+cosx+c when it should be x^2/2 + xsinx + cosx + c I believe. So I'm missing x^2/2... would really appreciate if someone could help. Thanks
2. (Original post by jordanwu)
Hi I've tried many times to integrate x(1+cosx) but I keep getting xsinx+cosx+c when it should be x^2/2 + xsinx + cosx + c I believe. So I'm missing x^2/2... would really appreciate if someone could help. Thanks
Split (expand) into x + x cos x

First term integrates to x^2/2.

Second term use IBP.
3. (Original post by jordanwu)
Hi I've tried many times to integrate x(1+cosx) but I keep getting xsinx+cosx+c when it should be x^2/2 + xsinx + cosx + c I believe. So I'm missing x^2/2... would really appreciate if someone could help. Thanks
Zacken has given you the correct method. But it may also be a good idea if you post you working showing how you got xsinx+cosx+c.

4. (Original post by Zacken)
Split (expand) into x + x cos x

First term integrates to x^2/2.

Second term use IBP.
Thanks!
5. (Original post by jordanwu)
Thanks!
No problem.

Edit: 4 hours later, just saw notnek's reply, I agree - it'd be helpful for you to post your answer so we can identify what conceptual mistake you are making.

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