Question

solve this integral
...................

.

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation: