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Grade: 12 
        
inegration of (sinx + cosx)/3+sin2x dx......................................
 
one year ago

Answers : (1)

Tech Xposed
37 Points 
							
The answer is:-
    	
  1. bring the denominator in (sin x – cosx)^2 format
    2. 	
  2. then take sin x- cos x= t
    3. 	
  3. therfore sin x + cos x dx = dt
    4. 	
  4. then the question will be converted into dt/a^2 – t^2 format then we can apply the formula.
\int \frac{sinx+cosx}{3+sin2x} =\int \frac{sinx+cosx}{4-1+sin2x} =\int \frac{sinx+cosx}{4-(1-sin2x)} =\int \frac{sinx+cosx}{4-(sin^{2}x+cos^{2}x-sin2x)} =\int \frac{sinx+cosx}{4-(sinx-cosx)^{2}} let sin x- cos x =t => (cos x +sin x )dx = dt =\int \frac{dt}{4-t^2} = \frac{1}{2*2} ln\frac{2+t}{2-t} = \frac{1}{2*2} ln\frac{2+sinx-cosx}{2-sinx+cosx}
one year ago
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