Help with Integral: c*Sin[ArcTan[f(t)]]

[FunkyDwarf]

Hey guys,

im completely stumped on this one. I had to go through several substitutions just to get it to this stage which is uninspiriring :P

Integral wrt t of c*Sin[ArcTan[(f(t)]] where f(t) is a linear function of t

Sorry, i can't use latex to save my life :p
-G

 

[Feldoh]

$$\int c*\sin{(\arctan{f(t))}} dt$$?

 

[arildno]

Remember:
$$x=tan(\arctan(x))=\frac{\sin(\arctan(x))}{\sqrt{1-\sin^{2}(\arctan(x)}}$$

Solve for sin(arctan(x))

 

[FunkyDwarf]

Ah yeh of course, i was worried about applying inverse sin to the top and bottom equally but you sort of can because you know what sine is from the substitution and so can get cos. Thanks!