If ∫$$1cos3$$⁡$$x2sin$$⁡$$2xdx=($$$$tan$$⁡$$x)A+C($$$$tan$$⁡$$x)B+k$$, where k is constant of integration then $$A+B+C$$ is

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If ∫$$1cos3$$⁡$$x2sin$$⁡$$2xdx=($$$$tan$$⁡$$x)A+C($$$$tan$$⁡$$x)B+k$$, where k is constant of  integration then $$A+B+C$$ is

Infinity Learn · Accepted Answer

$$I=$$∫$$dxcos3x2sin2x=$$∫$$dxcos3x2$$·$$2sinxcosx=12$$∫$$1cosx72$$.$$sinx12dx$$    $$=12$$∫$$dxsinxcosx12$$·$$cosx72+12$$  $$=12$$∫$$1($$$$tan$$⁡$$x)12$$⋅$$cos4$$⁡$$xdx=12$$∫$$1+tan2$$⁡$$x($$$$tan$$⁡$$x)12sec2$$⁡xdx $$=12$$∫$$1+t2t12dt$$ , where $$t=$$$$tan$$ x                                    $$dt=sec2x$$ $$dx=122t+25t52+k=($$$$tan$$⁡$$x)12+($$$$tan$$⁡$$x)525+k=($$$$tan$$⁡$$x)A+C($$$$tan$$⁡$$x)B+k$$  (Given) ∴ $$A=12$$ $$B=52$$ $$C=15$$∴$$A+B+C=12+52+15=165$$

$If \int \frac{1}{\cos^{3} x \sqrt{2 \sin 2 x}} d x = (\tan x)^{A} + C (\tan x)^{B} + k, where k is constant of integration then A + B + C is$

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If ∫1cos3⁡x2sin⁡2xdx=(tan⁡x)A+C(tan⁡x)B+k, where k is constant of integration then A+B+C is

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$If \int \frac{1}{\cos^{3} x \sqrt{2 \sin 2 x}} d x = (\tan x)^{A} + C (\tan x)^{B} + k, where k is constant of integration then A + B + C is$