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प्रश्न
Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`
उत्तर
Let I = `int_1^2 dx/(x^2 + 6x + 5)`
= `int_1^2 dx/(x^2 + 6x + 9 - 9 + 5)`
= `int_1^2 dx/((x + 3)^2 - (2)^2`
= `(1)/(2 x 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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