solve this integral
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Answered by
13
The answer is given below :
We know that,
e^(logx) = x.
Now,
e^(2 log cotx)
= e^{log (cotx)²}
= e^(log cot²x)
= cot²x
= cosec²x - 1
since cosec²x - cot²x = 1
Now,
∫ e^(2 log cotx) dx
= ∫ (cosec²x - 1) dx
= ∫ cosec²x dx - ∫ dx
= - cotx - x + c, where c is integral constant
which is the required solution.
Thus, option (4) is correct.
RULE :
∫ cosec²x dx = - cotx
Thank you for your question.
We know that,
e^(logx) = x.
Now,
e^(2 log cotx)
= e^{log (cotx)²}
= e^(log cot²x)
= cot²x
= cosec²x - 1
since cosec²x - cot²x = 1
Now,
∫ e^(2 log cotx) dx
= ∫ (cosec²x - 1) dx
= ∫ cosec²x dx - ∫ dx
= - cotx - x + c, where c is integral constant
which is the required solution.
Thus, option (4) is correct.
RULE :
∫ cosec²x dx = - cotx
Thank you for your question.
Answered by
5
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