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प्रश्न
Evaluate `int_1^2 (3x)/((9x^2 - 1)) "d"x`
उत्तर
Let I = `int_1^2 (3x)/((9x^2 - 1)) "d"x`
= `3int_1^2 x/(9x^2 - 1) "d"x`
Put 9x2 – 1 = t
∴ 18x dx = dt
∴ x dx = `1/18` dt
When x = 1, t = 9(1)2 – 1 = 8
When x = 2, t = 9(2)2 – 1 = 35
∴ I = `3int_8^35 1/"t"*"dt"/18`
= `1/6 int_8^35 "dt"/"t"`
= `1/6[log|"t"|]_8^35`
= `1/6(log 35 - log 8)`
∴ I = `1/6 log (35/8)`
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