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intdx/((2x-7)sqrt(x^2-7x+12) is equal to...

`intdx/((2x-7)sqrt(x^2-7x+12)` is equal to

A

`2sec^(-1)(2x-7)+C`

B

`sec^(-1)(2x-7)+C`

C

`(1)/(2)sec^(-1)(2x-7)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Let `I=int(1)/((2x-7)sqrt(x^(2)-7x+12))dx`
`rArrI=int(2)/((2x-7)sqrt(4x^(2)-28x+48))dx`
`rArr I=int(1)/((2x-7)sqrt((2x-7)^(2)-12))d(2x-7)=sec^(-1)(2x-7)+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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