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$\int \frac{e^{x} (1 + x)}{\cos^{2} (x e^{x})} d x .$

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Correct option is A

Letz=xex . Then dz=1ex+xexdx=ex(1+x)dx . Thus, ∫ex(1+x)cos2⁡xexdx=∫dzcos2⁡z=∫sec2⁡zdz=tan⁡z+c=tan⁡xex+c

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∫ex1+xcos2xexdx.

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$\int \frac{e^{x} (1 + x)}{\cos^{2} (x e^{x})} d x .$