Need help to Integrate cosy/((sin(^2)y)), Sorry for all the notation, just trying to make it clear.
R rhino4552 New member Joined Jun 13, 2011 Messages 4 Jun 14, 2011 #1 Need help to Integrate cosy/((sin(^2)y)), Sorry for all the notation, just trying to make it clear.
tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 11,339 Jun 14, 2011 #2 Substitution? u = sin(y), maybe?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Jun 14, 2011 #3 Hello, rhino4552! \(\displaystyle I \;=\;\int \frac{\cos y}{\sin^2y}\,dy\) Click to expand... \(\displaystyle \text{Note that: }\:\frac{\cos y}{\sin^2y} \;=\;\frac{1}{\sin y}\cdot\frac{\cos y}{\sin y} \;=\;\csc y\cot y\) \(\displaystyle \text{Therefore: }\:I \;=\; \int \csc y\cot y\,dy \;=\;-\csc y + C\)
Hello, rhino4552! \(\displaystyle I \;=\;\int \frac{\cos y}{\sin^2y}\,dy\) Click to expand... \(\displaystyle \text{Note that: }\:\frac{\cos y}{\sin^2y} \;=\;\frac{1}{\sin y}\cdot\frac{\cos y}{\sin y} \;=\;\csc y\cot y\) \(\displaystyle \text{Therefore: }\:I \;=\; \int \csc y\cot y\,dy \;=\;-\csc y + C\)
