If $$f(x)=1cos2$$⁡$$x1+$$$$tan$$⁡x then its $$anti-derivative$$ $$F(x)$$ ,$$F(0)$$ $$=$$ $$4$$ is

Correct option is 32(1+tan⁡x+1)

Questions

If $f (x) = \frac{1}{\cos^{2} x \sqrt{1 + \tan x}}$ then its anti-derivative $F (x), F (0) = 4$ is

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1+tan⁡x+4

23(1+tan⁡x)3/2

2(1+tan⁡x+1)

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detailed solution

Correct option is C

F(x)=∫dxcos2⁡x1+tan⁡x+C=∫11+tdt+C(t=tan⁡x)=2(1+t)+C=21+tan⁡x+CSince 4=F(0)=2+C⇒C=2 HenceF(x)=2(1+tan⁡x+1)

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If f(x)=1cos2⁡x1+tan⁡x then its anti-derivative F(x) ,F(0) = 4 is

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If $f (x) = \frac{1}{\cos^{2} x \sqrt{1 + \tan x}}$ then its anti-derivative $F (x), F (0) = 4$ is