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Evaluate: int(6x+7)/(sqrt((x-5)(x-4)))\ ...

Evaluate: `int(6x+7)/(sqrt((x-5)(x-4)))\ dx`

Text Solution

Verified by Experts

`I=∫(6x+7√)/((x−5)(x−4))dx`
`=∫(6x+7)/(√x^2−9x+20)dx`
Let `6x+7=Ad/(dx)(x^2−9x+20)+B`
`⇒6x+7=A(2x−9)+B⇒6x+7=2Ax+(−9A+B)`
On equating the coefficients of x and constant term on both sides, we get
`2A=6⇒A=3` and
`−9A+B=7⇒B=34`
So,
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