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AP EAMCET · Maths · Indefinite Integration

If f(x)=1cos2x1+tanx, then its anti-derivative F(x)=       , given F(0)=4

  1. A 1+tanx+4
  2. B 23(1+tanx)3/2
  3. C 2(1+tanx+1)
  4. D 1+tanx+2
Verified Solution

Answer & Solution

Correct Answer

(C) 2(1+tanx+1)

Step-by-step Solution

Detailed explanation

⇒fx=1cos2x1+tanx put 1+tanx=t ⇒1·sec2x2·1+tanx=dtdx ⇒dx=21+tanxsec2xdt ⇒∫fxdx=∫1cos2x1+tanxdx ⇒∫fxdx=∫21+tanxsec2x·cos2x·1+tanxdt ⇒Fx=∫2dt ⇒Fx=2t+C ⇒Fx=21+tanx+C…