Evaluate ഽ sin (log x) + cos (log x) dx

Evaluate \(\int { \frac { \left( { x }^{ 2 }+1 \right) dx }{ { \left( x-1 \right) }^{ 2 }\left( x+3 \right) } } \)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx\)

Prove that \(\int _{ a }^{ b }{ \frac { f\left( x \right) }{ f\left( x \right) +f(a+b-x) } } dx=\frac { b-a }{ 2 } \)

Using integrals as limit of sums, evaluate \(\int _{ 2 }^{ 4 }{ (2x-1) } dx\)