Question

Integrat this.. (3 sinx-2) cosx/5- cos square x-4 sinx

Answer 1

int ( 3sinx-2) cosx /( 5- cos^2x - 4 sinx) dx [ let sinx = t so cos dx = dt ]
= int (3t -2) dt/ ( 5-1 + t^2 - 4t)
= int( 3t -2 )/(t^2 - 4t + 4) dt
= int ( 3t -2 )/( t-2)^2 dt
= int 3t/( t-2 )^2 dt -2int /(t-2)^2 dt
= int 3/(t-2) dt + 6 intdt/(t-2)^2 - 2int dt/(t- 2)^2
= 3 log ( t-2) - 4/( t-2) +C
= 3 log ( sinx - 2 ) -- 4/( sinx -2 ) + C