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$\int \frac{e^{x} (1 + x)}{\cos^{2} (e^{x} x)} dx$ is equal to

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−cot⁡exx+C

tan⁡xex+C

tan⁡ex+C

cot⁡ex+C

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detailed solution

Correct option is B

∫ex(1+x)cos2⁡exxdx Let xex=t⇒xex+ex=dtdx⇒dx=dtex(x+1)∴∫ex(1+x)cos2⁡exxdx=∫ex(1+x)cos2⁡t×dtex(1+x)=∫1cos2⁡tdt=∫sec2⁡tdt=tan⁡t+C=tan⁡xex+C

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∫ex(1+x)cos2⁡exxdx is equal to

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$\int \frac{e^{x} (1 + x)}{\cos^{2} (e^{x} x)} dx$ is equal to