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प्रश्न
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate:
`∫ 1/(4x^2 − 20x + 17) dx`
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उत्तर
Let I = `int 1/(4x^2 - 20x + 17)` dx
= `1/4 int 1/(x^2 - 5x + 17/4)` dx
= `1/4 int 1/(x^2 - 2 * 5/2 x + 25/4 - 25/4 + 17/4)` dx
= `1/4 int 1/((x - 5/2)^2 - 8/4)` dx
= `1/4 int 1/((x - 5/2)^2 - (sqrt2)^2)` dx
= `1/4 xx 1/(2sqrt2) log |(x - 5/2 - sqrt2)/(x - 5/2 + sqrt2)|` + c
∴ I = `1/(8sqrt2) log |(2x - 5 - 2sqrt2)/(2x - 5 + 2sqrt2)|` + c
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