# Help with an integral

1. Jun 14, 2008

### 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 cant use latex to save my life :p
-G

2. Jun 14, 2008

### Feldoh

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

3. Jun 14, 2008

### arildno

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

Solve for sin(arctan(x))

4. Jun 16, 2008

### 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!