Question

integral (cos(5 x)+sin(10 x))/(sin(5 x)) dx

I got 1/5 (2 sin(5 x)+log(sin(5 x)))+constant but it's wrong

Answer 1

\[\frac{1}{5} \text{Log}[\text{Sin}[5 x]]+\frac{2}{5} \text{Sin}[5 x] \]

Answer 2

Distribute the sin(5x) and break the integral up.
\[\int\limits \cot(5x)dx+\int\limits \frac{\sin(10x)}{\sin(5x)}dx\]
Rewrite using the double angle identity.
\[\int\limits \cot(5x) dx+2 \int\limits \frac{\sin(5x)\cos(5x)}{\sin(5x)}dx\]
Go from there :P

Answer 3

\[\frac {\cos(5x)+\sin(10x)}{\sin(5x)} = \cot(5x)+\frac{2\sin(5x)\cos(5x)}{\sin(5x)}\]
\[= \cot(5x)+2\cos(5x)\]
Integrating this is much easier :)

Answer 4

I integrated those, and got the above answer same as robtobey... I guess the answer is wrong then... I am not sure

Answer 5

http://www.wolframalpha.com/input/?i=integral+of+(cos(5x)%2Bsin(10x))%2Fsin(5x)+dx

Answer 6

thanks guys :)... I am not sure how to click good answers but you guys are great

Answer 7

A jpg of the solution with steps is attached. Sorry it took so long. This site will not accept a tiff file as an attachment.