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प्रश्न
Evaluate \[\int\operatorname{cosec}x(\operatorname{cosec}x+\cot x)\,dx.\]
पर्याय
\[\cot x+\operatorname{cosec}x+C\]
\[-\cot x-\operatorname{cosec}x+C\]
\[\tan x-\sec x+C\]
\[-\cot x+\operatorname{cosec}x+C\]
MCQ
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उत्तर
Expand the integrand as \[\operatorname{cosec}^2x+\operatorname{cosec}x\cot x.\] Their antiderivatives are \[-\cot x\] and \[-\operatorname{cosec}x\], respectively.
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