Question

Evaluate \[\int\operatorname{cosec}x(\operatorname{cosec}x+\cot x)\,dx.\]

Options

• \[\cot x+\operatorname{cosec}x+C\]

• \[-\cot x-\operatorname{cosec}x+C\]

• \[\tan x-\sec x+C\]

• \[-\cot x+\operatorname{cosec}x+C\]

Answer 1

Expand the integrand as \[\operatorname{cosec}^2x+\operatorname{cosec}x\cot x.\] Their antiderivatives are \[-\cot x\] and \[-\operatorname{cosec}x\], respectively.