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Question
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Options
− cot (exx) + C
tan (xex) + C
tan (ex) + C
cot (ex) + C
Solution
`int (e^x(1 +x))/cos^2(e^x x) dx` equals tan (xex) + C.
Explanation:
Let `int (e^x (1 + x))/(cos^2 (e^x x)) dx`
Put xex = t
⇒ `(e^x *1 + e^x x) dx = dt`
ex (1 + x) dx = dt
`I = int dt/(cos^2 t) = sec^2` t dt
= tan t + C
= tan (xex) + C
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