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int(e^x(1+x))/(cos^2(x e^x))\ dx= 2(log...

`int(e^x(1+x))/(cos^2(x e^x))\ dx=` `2(log)_ecos(x e^x)+C` (b) `sec(x e^x)+C` (c) `tan(x e^x)+C` (d) `tan(x+e^x)+C`

A

`tan(xe^(x))+C`

B

`cot(xe^(x))+C`

C

`ex^(x)tanx+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Put `xe^(x)=t and(xe^(x)+e^(x))dx=dt`.
`:." "I=int(1)/(cos^(2)t)dt=intsec^(2)"t dt"=tan t+C`.
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