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Evaluate: int1/(x\ {6\ (logx)^2+7logx+2}...

Evaluate: `int1/(x\ {6\ (logx)^2+7logx+2})\ dx`

Text Solution

Verified by Experts

`I=int frac{d x}{x{6(log x)^{2}+7 log x+2}}`
Putting `log x=t`
`Rightarrow frac{1}{x} d x=d t `
`therefore I=int frac{d t}{6 t^{2}+7 t+2} `
`=int frac{d t}{(3 t+2)(2 t+1)}`
Let `frac{1}{(3 t+2)(2 t+1)}=frac{A}{3 t+2}+frac{B}{2 t+1}`
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