JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

If $\displaystyle\int\frac{dx}{\cos^3x\sqrt{2\sin2x}}=(\tan x)^A+C(\tan x)^B+k$ , where k is a constant of integration, then A + B + C equals :

\dfrac{21}5

\dfrac{16}5

\dfrac7{10}

\dfrac{27}{10}

Answer and worked solution

Official answer: B

$\cos^3x\sqrt{2\sin2x}=2\cos^4x\sqrt{\tan x}$ , so with $t=\tan x$ the integral is $\int\frac{1+t^2}{2\sqrt t}dt=t^{1/2}+\frac15t^{5/2}$ . So $A=\frac12$ , $B=\frac52$ , $C=\frac15$ , and the sum is $\frac{16}5$ .

Topics:Substitution

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 74