Indefinite integral:

Question

luigi0210 · Answer

luigi0210 · Answer

@zepdrix you available for help? >.<

zepdrix · Answer

Ahhh the kitty! >.< the cuteness is killing me...

zepdrix · Answer

$$\Large\rm \int\limits \frac{\sin 46x}{1+(\cos 46x)^2}dx$$

$$\Large\rm u=\cos 46x$$

luigi0210 · Answer

Poor Zepdrix :P

That'll leave us with $\large \int \frac{du}{1+u^2}$ right?

zepdrix · Answer

Ummm you should be getting a -1/46 somewhere also.
From your du, yes?

zepdrix · Answer

$$\Large\rm du=-46 \sin 46x~dx$$

luigi0210 · Answer

Oh, right, sorry I'm too tired >.< 
$$\LARGE -\frac{1}{46} \int \frac{du}{1+x^2}$$?

zepdrix · Answer

Mmmmm k, good.
Does that look familiar? :)

It's a good integral to put to memory!!

luigi0210 · Answer

Wait, isn't it just 1/46, not negative? 

That's where I'm stuck.. haven't done this long :/

zepdrix · Answer

Derivative of cosine is minus sine yes? :o

luigi0210 · Answer

Yes, but we're integrating cosine, not differentiating it >.<

zepdrix · Answer

We're making a substitution,
We're differentiating it to get our du.

:o

luigi0210 · Answer

Ohh, sorry I thinking of something else ._. 

And $\large \int \frac{1}{1+x^2}=arctanx+C$?

zepdrix · Answer

Yes.

luigi0210 · Answer

Then just sub back in.. thank you zepdrix!

zepdrix · Answer

yay team \c:/