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Evaluate : int((1)/(ax + b)) dx....

Evaluate : `int((1)/(ax + b)) dx.`

A

`(1)/(alpha) log_e (a +b)+c`

B

`(1)/(alpha)^2 log_e (ax +b)^2+c`

C

`(1)/(alpha) log_e (ax +b)+c`

D

`(1)/(alpha) log_e (ax +b)^2+c`

Text Solution

Verified by Experts

The correct Answer is:
C
Put ax + b =z. Then, `(d)/(dx) (ax +b ) = (dz)/(dx) or a dx =dz or dx = (dz)/(a)`
`:. Int (1)/((ax +b)) dx = int (1)/(z) (dz)/(a) = (1)/(alpha) int (dz)/(z) = (1)/(z) = (1)/(alpha) log. Z+c = (1)/(alpha) log_e (ax +b)+c`
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