Z zooba New member Joined Feb 18, 2015 Messages 7 Feb 18, 2015 #1 \(\displaystyle \displaystyle{ \int \, }\) \(\displaystyle \dfrac{y\cdot \sin(y)\, -\, \cos(y)}{\sin(y)\, +\, y\cdot \cos(y)}\) i tried to integrate this function but with no use. Last edited by a moderator: Feb 18, 2015
\(\displaystyle \displaystyle{ \int \, }\) \(\displaystyle \dfrac{y\cdot \sin(y)\, -\, \cos(y)}{\sin(y)\, +\, y\cdot \cos(y)}\) i tried to integrate this function but with no use.
I Ishuda Elite Member Joined Jul 30, 2014 Messages 3,342 Feb 18, 2015 #2 zooba said: \(\displaystyle \displaystyle{ \int \, }\) \(\displaystyle \dfrac{y\cdot \sin(y)\, -\, \cos(y)}{\sin(y)\, +\, y\cdot \cos(y)}\) i tried to integrate this function but with no use. Click to expand... I'm not sure it helps but if f(y) = sin(y) + y cos(y) then you have \(\displaystyle \displaystyle{ \int \,}\)\(\displaystyle \dfrac{y sin(y) \,-\, cos(y)}{sin(y) \,+\, y cos(y)}\, dy \,=\, -\ln[|f(y)|] \,+\,\) \(\displaystyle \displaystyle{ \int \,}\) \(\displaystyle \dfrac{1}{y \,+\, tan(y)}\, dy\) I'm not sure the latter integral has a closed form solution. Last edited by a moderator: Feb 18, 2015
zooba said: \(\displaystyle \displaystyle{ \int \, }\) \(\displaystyle \dfrac{y\cdot \sin(y)\, -\, \cos(y)}{\sin(y)\, +\, y\cdot \cos(y)}\) i tried to integrate this function but with no use. Click to expand... I'm not sure it helps but if f(y) = sin(y) + y cos(y) then you have \(\displaystyle \displaystyle{ \int \,}\)\(\displaystyle \dfrac{y sin(y) \,-\, cos(y)}{sin(y) \,+\, y cos(y)}\, dy \,=\, -\ln[|f(y)|] \,+\,\) \(\displaystyle \displaystyle{ \int \,}\) \(\displaystyle \dfrac{1}{y \,+\, tan(y)}\, dy\) I'm not sure the latter integral has a closed form solution.
