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int(1+tanx)/(e^(-x)cosx)dx is equal to...

`int(1+tanx)/(e^(-x)cosx)dx` is equal to

A

`e^(-x)tanx+C`

B

`e^(-x)secx+C`

C

`e^(x)sec x+C`

D

`e^(x)tanx+C`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int e^(x) sec x dx +int e^(x) sec x tan x dx`
On integration by parts, we get
`e^(x)secx - int e^(x) sec x tan x dx+int e^(x)sec x tan x dx+C`
`=e^(x)secx+C`
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