(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi there. I'm confused about this exercise. It asks me to solve the integral using integration by parts. And the integral is:

[tex]\displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx[/tex]

3. The attempt at a solution

What I did:

[tex]u=3x[/tex]

[tex]du=3dx[/tex]

[tex]dv=cos(\displaystyle\frac{x}{2})[/tex]

[tex]v=\sin(\displaystyle\frac{x}{2})[/tex]

Then:

[tex]\displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx=3x\sin(\displaystyle\frac{x}{2})-\displaystyle\int_{}^{}\sin(\displaystyle\frac{x}{2})3dx=3x\sin(\displaystyle\frac{x}{2})-3\cos(\displaystyle\frac{x}{2})[/tex]

And derive gives me:

[tex]\displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx=12\cos(\displaystyle\frac{x}{2})+6x\sin(\displaystyle\frac{x}{2})[/tex]

So I think I'm doing something wrong, but I don't know what. And actually in my first attempt to a solution I got something like: [tex]\displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx=\displaystyle\frac{1}{3}[x\sin(\displaystyle\frac{x}{2})-\cos(\displaystyle\frac{x}{2})][/tex], I arrived to this result by first taking the 3 out of the integral, and passing it to the other side at the end.

Any help will be thanked.

Bye there.

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# Homework Help: Integration by parts

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