ज्ञात करें `int(1)/(5 cos x - 12 sin x)dx`

Explanation

`int(dx)/(5 cos x - 12 sin x)`
`5=4sinalpha, 12 = r cos alpha` रखे
तो, `5 cos x -12 sin x =r ( sin alphacosx - cos alphasin x)`
`=rsin(alpha-x)=-rsin(x-alpha)`
जहां `r=sqrt(5^2+12^@)=13` तथा `tanalpha=5/12` या `alpha=tan^(-1)(5/12)`
अब, `I=-1/13 int (dx)/(sin(x-alpha))=-1/13 int " cosec(x-alpha)dx`
`=-1/13"log |" cosec "( x - alpha)-cot(x-alpha)|+c,` जहां `alpha=tan^(-1)(5/12)