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

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−2cotex+C

2cotex+C

−2cotex+C

2cotex+C

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detailed solution

Correct option is A

Let I=∫cos⁡ec2exexxdx Put ex=y2exxdx=dyI=2∫cos⁡ec2ydy=2(−cot⁡y)+CI=−2cot⁡ex+C

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∫cos⁡ec2exexdxx is equal to

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