`=int (dx)/(a cos x+ b sin x)=(1)/(r) In[tan((x+alpha)/(2))]` के रूप का है।
`r` बराबर है।

Options

A. `a^(2)+b^(2)`
B. `sqrt(a^(2)+b^(2))`
C. `a+b`
D. `sqrt(a^(2)-b^(2))`

Explanation

`I= int (dx)/(a cos x b sin x)`

`:. alpha= r sin alpha` तथा `b= r cos alpha` रखने पर

`I= (1)/(r) (dx)/(sin alpha* cos x+ cos alpha* sin x)`

`=(1)/(r) int (dx)/(sin (x+alpha))=(1)/(r) int "cosec" (x+alpha)dx`

`=(1)/(r) ln [ "cosec" (x+alpha)-cot (x+alpha)]+C`

`=(1)/(r)ln [(1)/(sin(x+alpha))-(cos(x+alpha))/(sin(x+alpha))]+C`

`=(1)/(r)ln [(1-cos (x+alpha))/(sin (x+alpha))]+C`

`=(1)/(r)ln [(2sin^(2)((x+alpha)/(2)))/(2 sin ((x+alpha)/(2))*((x+alpha)/(2)))]+C`

`=(1)/(r)ln [ tan((x+alpha)/(2))]+C`

`r=sqrt(a^(2)+b^(2)`