More integration by subsitution

[mbrmbrg]

I (now) know that I can check the following by differentiating my answer, but I don't trust my differentiation.

Problem is as follows:

$$\int\tan^4{3x}\sec^2{3x}dx$$
I assigned u=tan(3x), du=3sec^2(3x) and got that integral in terms of u:
$$\frac{1}{3}\int u^4du$$
$$=\frac{1}{3}\times\frac{u^5}{5}+C$$
$$=\frac{\tan^5(3x)}{15}+C$$

I think that differentiates into what's in the original integral, but as I haven't differentiated anything that looks like that for a while now, I'd appreciate some feedback.

Thanks!

 

[courtrigrad]

thats correct

 

[mbrmbrg]

Thank you very much.