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प्रश्न
Solve the following : `int_2^4 x/(x^2 + 1)*dx`
उत्तर
Let I = `int_2^4 x/(x^2 + 1)*dx`
Put x2 + 1 = t
∴ 2x·dx = dt
∴ x·dx = `"dt"/(2)`
When x = 2, t = 22 + 1 = 5
When x = 4, t = 42 + 1 = 17
∴ I = `int_5^17 (1)/"t"*"dt"/2`
= `(1)/(2) int_5^17 "dt"/"t"`
= `(1)/(2)[log|"t"|]_5^17`
= `(1)/(2)(log 17 - log 5)`
∴ I = `(1)/(2)log (17/5)`.
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