Integer Question 2

$\Rightarrow 21_{1}=-\operatorname{cosec} x \cot x+\ln \left|\tan \frac{x}{2}\right|$
$\Rightarrow I_{1}=-\frac{1}{2} \operatorname{cosec} x \cot x+\frac{1}{2} \ln \left|\tan \frac{x}{2}\right|$
From (1), $4 I=-\cot x \operatorname{cosec}^{3} x-\frac{3}{2} \operatorname{cosec} x \cot x+\frac{3}{2} \ln \left|\tan \frac{x}{2}\right|+4 c$
$I=-\frac{1}{4} \operatorname{cosec} x \cot x\left(\operatorname{cosec}^{2} x+\frac{3}{2}\right)+\frac{3}{8} \ln \left|\tan \frac{x}{2}\right|+c$
$\therefore \alpha=-\frac{1}{4}, \beta=\frac{3}{8} \Rightarrow 8(\alpha+\beta)=1$

Sol.(B)

Integer Question 2

Integer Question 1

Indefinite Integration Question 1

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