1.

Solve this integral ....................

Answer»

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.


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