Question

Integrate sin2x/(a+bcosx)^2

Answer 1

I=-1/2cot(x/2)-1/2cot(x/2)3]

Answer 2

Step-by-step explanation:

integration of sin2x/(a+bcosx) ^2

we know sin2x=2sinxcosx

so, integration of 2sinxcosx/(a+bcosx)^2dx

a+bcosx=y

-bsinx(1)=dy/dx

-bsinxdx=du

dx=-dy/bsinx

integration of 2sinxcosx/y^2×(-dy/bsinx)

integration of 2sinxcosx(-dy)/y^2bsinx eqn no. 1

-2/b integration of cosx(dy) /y^2

let a+b cosx =y

cosx= y- a/b

put in eqn no. 1

-2/b integration of 1/y^2(y-a/b) dy

-2/b^2 integration of (y/y^2-a/y^2) dy

-2/b^2 integration of (1/y-a/y^2) dy

-2/b^2(log y + a/y) +c

-2/b^2(log|a+bcosx|+ a/a+bcosx + C