∫$$cot$$⁡ex⋅$$cos$$⁡$$ec2ex$$⋅exdx is equal to

Correct option is 3−12cotex2+C

Questions

$\int \cot (e^{x}) \cdot \cos e c^{2} (e^{x}) \cdot e^{x} d x is equal to$

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−2cotex+C

2cotex+C

−12cotex2+C

12cotex+C

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detailed solution

Correct option is C

Let I=∫cot⁡ex⋅cos⁡ec2ex⋅exdx Let ex=yexdx=dyI=∫cot⁡y⋅cos⁡ec2ydy Put cot⁡y=zcos⁡ec2ydy=−dzI=∫z⋅(−dz)=−z22+C=−12(cot⁡y)2+C=−12cot⁡ex2+C

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∫cot⁡ex⋅cos⁡ec2ex⋅exdx is equal to

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$\int \cot (e^{x}) \cdot \cos e c^{2} (e^{x}) \cdot e^{x} d x is equal to$