Let, 
At 
At 
Use integration by parts
![\[\int I\times IIdt=I\int IIdt-\int \frac{d}{dt}I\left( \int IIdt \right)dt\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-538e517f6a7337e644eecf9e2eda6963_l3.png "Rendered by QuickLaTeX.com")
![\[y=t\int \cot tdt-\int \frac{d}{dt}t\left( \int \cot tdt \right)dt\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-01ff57ef0f334e11d9219aafae389542_l3.png "Rendered by QuickLaTeX.com")
![\[y=\left( t\log \sin t \right)_{0}^{\pi /2}-\int _{0}^{\pi /2}\log \sin tdt\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4bb31ca6815f0577683a99afbf09d797_l3.png "Rendered by QuickLaTeX.com")
Let,
![\[I=\int _{0}^{\pi /2}\log \sin tdt......(1)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8b3385ac0deb6ebceacc8d1fda6cb0b8_l3.png "Rendered by QuickLaTeX.com")
Use king theorem of definite integral
Adding equation (1) and (2)
Let, 
At 
At 
Let,
At
At
Use integration by parts
Let,
Use king theorem of definite integral
Adding equation (1) and (2)
Let,
At
At
