Indefinite IntegrationHard

Question

The value of cosec2 x dx is equal to:

Options

A.cot x - cot-1 x + C
B.C - cot x + cot-1 x
C.- tan-1 x - + C
D.-eln tan-1x - cot x + C

Solution

cosec2 x dx
= ∫cos ec2 xdx - = - cotx - tan-1x + C
= - cotx - cot-1x + C         ....... (1)
= - tan-1 x - + C      ....... (2)
= - eln tan-1x - cotx + C        ....... (3)

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