What is the simplified form of the integral (csc^4 3\theta)(tan^4 3\theta)?

[rjs123]

Homework Statement

$$\int\sec^4 3\theta$$

 

[Mark44]

Have you tried anything? Hint d/dt(tan(t)) = sec²(t)

 

[Dickfore]

Hint:

$$\sec^{4}{(3 \theta)} = \sec^{2}{(3 \theta)} \, \sec^{2}{(3 \theta)} = <br /> (1 + \tan^{2}{(3 \theta)}) \, \sec^{2}{(3 \,\theta)}$$

and use the substitution:

$$x = \tan{(3 \theta)}$$

 

[rjs123]

thanks guys...i knew it was something simple.

The original problem was:

$$\int(csc^4 3\theta)(tan^4 3\theta)$$

simplified this to:

$$\int\sec^4 3\theta$$

and now i know how easy the rest was.