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inte^(tanx)(sinx-secx)dx is equal to...

`inte^(tanx)(sinx-secx)dx` is equal to

A

`e^(tanx)cosx +C`

B

`e^(tanx)sinx +C`

C

`-e^(tanx)cosx +C`

D

`e^(tanx)sec x +C`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=inte^(tanx)(sinx-secx)dx`
`=int sinx e^(tanx)dx-int secx e^(tanx)dx`
`=-e^(tanx)cosx+int cos x e^(tanx)sec^(2)x dx-int sec x e^(tanx) dx`
`= -cosx e^(tanx) +C`
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