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

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tan(xex)+c

tan(ex)+c

tan(x+ex)+c

sec(ex)+c

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detailed solution

Correct option is A

Let z=xex. Then dz=1ex+xexdx=ex1+xdx . Thus, ∫ex(1+x)cos2⁡xexdx=∫dzcos2⁡z =∫sec2⁡zdz =tan⁡z+c=tan⁡xex+c

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Evaluate ∫ex(1+x)cos2⁡xexdx

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