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Find the value of ∫ cosec x (cot x - cosec x) dx

Find the value of ∫ cosec x (cot x - cosec x) dx Correct Answer cot x - cosec x + C

Concept:

Some useful formulas are:

 ∫ cosecx.cotx dx = - cosecx + C

 ∫ cosec2x dx = - cotx + C

Calculation:

∫ cosecx(cotx - cosecx) dx

= ∫ cosecx.cotx dx - ∫ cosec2x dx

= - cosec x - (-cot x) + C, where C is the constant of integration

= cot x - cosec x + C

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