Question
$\int_0^1 {\frac{{\log x}}{{\sqrt {1 - {x^2}} }}\,dx = } $
$\int_0^1 {\frac{{\log x}}{{\sqrt {1 - {x^2}} }}dx }$
$={ \int_0^{\pi /2} {\frac{{\log \sin \theta .\cos \theta }}{{\cos \theta }}} } \,d\theta $
$ = \int_0^{\pi /2} {\,\log \sin \theta } \,d\theta = - \frac{\pi }{2}\log 2$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.