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int(0)^(pi//4)(e^(tanx))/(cos^(2)x)dx=?...

`int_(0)^(pi//4)(e^(tanx))/(cos^(2)x)dx=?`

A

`(e-1)`

B

`(e+1)`

C

`((1)/(e)+1)`

D

`((1)/(e)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(0)^(pi//4)e^(tanx)sec^(2)xdx=[e^(t)dt]_(0)^(1)`, where `tanx=t`.
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