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ans4.4=> I = integral 5/(x2+4)(x2+9) = integral k let x2 = t then k = 5/(t+4)(t+9) using partial fractions we get k = 1/t+4 - 1/t+9 now integral becomes I = 1/t+4 - 1/t+9 = [1/x2+4 - 1/x2+9]dx limit from 0 to infinity I = 1/2 tan-1x/2 - 1/3 tan-1x/3 lim 0 to infinity I = 1/2 * pi/2 - 1/3 * pi/2 = pi/12 option b) is correct
ans4.4=>
I = integral 5/(x2+4)(x2+9) = integral k
let x2 = t then
k = 5/(t+4)(t+9)
using partial fractions we get
k = 1/t+4 - 1/t+9
now integral becomes
I = 1/t+4 - 1/t+9 = [1/x2+4 - 1/x2+9]dx limit from 0 to infinity
I = 1/2 tan-1x/2 - 1/3 tan-1x/3 lim 0 to infinity
I = 1/2 * pi/2 - 1/3 * pi/2 = pi/12
option b) is correct
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