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प्रश्न
Evaluate:
`int_1^2 1/(x^2 + 6x + 5) dx`
Evaluate:
`int_1^2 (dx)/(x^2 + 6x + 5)`
मूल्यांकन
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उत्तर
Let I = `int_1^2 1/(x^2 + 6x + 5)`
= `int_1^2 (dx)/(x^2 + 6x + 9 - 9 + 5)`
= `int_1^2 (dx)/((x + 3)^2 - 4)`
= `int_1^2 (dx)/((x + 3)^2 - (2)^2)`
= `1/(2 xx 2)[log|(x + 3 - 2)/(x + 3 + 2)|]_1^2`
= `1/4[log|(x + 1)/(x + 5)|]_1^2`
= `1/4[log(3/7) - log(2/6)]`
= `1/4 log(3/7 xx 6/2)`
∴ I = `1/4 log(9/7)`
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