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AP EAMCET · Maths · Indefinite Integration

x+sinx1+cosxdx=

  1. A loge(1+cosx)+c
  2. B xsin2x2+c
  3. C tanx2+c
  4. D xtanx2+c
Verified Solution

Answer & Solution

Correct Answer

(D) xtanx2+c

Step-by-step Solution

Detailed explanation

Consider I=∫x+sinx1+cosxdx ⇒I=∫x1+cosxdx+∫sinx1+cosxdx Consider I=I1+I2 Now, I1=∫x1+cosxdx=∫xdx2cos2x2 ∵1+cosθ=2cos2θ2 ⇒I1=∫x2sec2x2dx ⇒I1=2x2tanx2-2logesecx2+c1…