1. integration by parts

I am stuck on how to do these types of problems by using integration by parts.

intergral sign xsec^2(3x)dx
I set fprime to sec^2(3x)
I set g = x, gprime = 1.
I dont know what f equals in this scenario and dont know how to solve it. Thanks.

2. Originally Posted by davecs77
I am stuck on how to do these types of problems by using integration by parts.

intergral sign xsec^2(3x)dx
I set fprime to sec^2(3x)
I set g = x, gprime = 1.
I dont know what f equals in this scenario and dont know how to solve it. Thanks.
As $\frac{d}{dx}\tan(x)=\sec^2(x)$, we have:

$\frac{1}{3}\frac{d}{dx}\tan(3x)=\sec^2(3x)$.

RonL

3. Originally Posted by CaptainBlack
As $\frac{d}{dx}\tan(x)=\sec^2(x)$, we have:

$\frac{1}{3}\frac{d}{dx}\tan(3x)=\sec^2(3x)$.

RonL
How would you solve the problem then?

4. Let $u=x, \;\ dv=sec^{2}(3x)dx, \;\ du=dx, \;\ v=\frac{tan(3x)}{3}$

$uv-\int{v}du$

$\frac{xtan(3x)}{3}-\frac{1}{3}\int{tan(3x)}dx$

Now, continue?.