∫0π/25tanx−3cotxtanx+cotxdx=

I=∫0π/2 5tan⁡x−3cot⁡xtan⁡x+cot⁡xdx------1I=∫0π/2 5tan⁡π2−x−3cot⁡π2−xtan⁡π2−x+cot⁡π2−xdxI=∫0π/2 5cot⁡x−3tan⁡xcot⁡x+tan⁡xdx----2(1)+(2)⇒2I=∫0π/2 2tan⁡x+2cot⁡xcot⁡x+tan⁡xdx=∫0π/2 2dx=2∫0π/2 (1)dx=2(x)0π/2=2π2=π⇒I=π2