-1-tan x1-tan 2 x-2 tan x d x equal to

The correct option is C log tan^2 x+√(tan x)+c ∫1/2 sin x cos xdx +1/2∫√(tan x)/sin x cos xdx =1/2∫sin^2 x+cos^2 x/sin x cos xdx +1/2∫sec^2 x/√(tan x)dx=log ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 3

∫1+√tan x1+ta...

Question

$\int \frac{(1 + \sqrt{t a n x}) (1 + t a n^{2} x)}{2 t a n x} d x$ equal to

l o g t a n^{2} x + \sqrt{t a n x} + c

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l o g t a n^{2} x + \frac{1}{2 \sqrt{t a n x}} + c

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l o g | t a n x | + 2 \sqrt{t a n x} + c

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l o g | t a n x | + \sqrt{t a n x} + c

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Solution

The correct option is A $l o g t a n^{2} x + \sqrt{t a n x} + c$

$\int \frac{1}{2 s i n x c o s x} d x + \frac{1}{2} \int \frac{\sqrt{t a n x}}{s i n x c o s x} d x = \frac{1}{2} \int \frac{s i n^{2} x + c o s^{2} x}{s i n x c o s x} d x + \frac{1}{2} \int \frac{s e c^{2} x}{\sqrt{t a n x}} d x = l o g (t a n^{2} x) + \sqrt{t a n x} + c$

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∫(1+√tanx)(1+tan2x)2tanxdx equal to

The correct option is A logtan2x+√tanx+c ∫12sinxcosxdx+12∫√tanxsinxcosxdx=12∫sin2x+cos2xsinxcosxdx+12∫sec2x√tanxdx=log(tan2x)+√tanx+c

$\int \frac{(1 + \sqrt{t a n x}) (1 + t a n^{2} x)}{2 t a n x} d x$ equal to