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int(e^x(1+x)/(cos^2(e^xx)dx equals (A) -...

`int(e^x(1+x)/(cos^2(e^xx)dx` equals (A) `-cot(e x^x)+C` (B) `tan(x e^x)+C` (C) `tan(e^x)+C` (D) `cot(e^x)+C`

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Verified by Experts

The correct Answer is:
b
`int (e^(x) (1+x))/(cos^(2) (e^(x)x))dx " "underset(rArr e^(x) (1+x)dx=dt)underset(rArr (e^(x) +xe^(x))dx=dt)("Let " e^(x) .x=t)`
` = int (1)/(cos^(2)t) dt = int sec^(2) t dt`
` = tan t+c = tan (xe^(x)) +c`
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