`(1)/(sinx cos^(3)x)`

Explanation

`int(1)/(sinx. Cos^(3)x)dx`
`=int(1)/((sinx)/(cosx).cos^(4)x)dx=int(sec^(4)x)/(tanx)dx`
`=int((1+tan^(2)x))/(tanx).sec^(2)x dx" "{:("माना "tanx=t),(rArr sec^(2)xdx=dt):}`
`=int(1+t^(2))/(t).dt=int((1)/(t)+t)dt`
`=log|t|+(t^(2))/(2)+c`
`=log|tanx|+(1)/(2)tan^(2)x+c`