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Prove the above integral. Prove the above integral.
Prove the above integral.
put : x2 + 1/x2 = t (2x - 2)/x3 .dx = dt 2(x4-1)x3.dx=dt I = integral of { (x4-1)/x2*x(x2+1+(1/x2)) .dx } = integral of { (1/2.(t)1/2 ).dt } = 1/2 * 2*(t)1/2 + C = (x2 + (1/x2) +1)1/2 + C --
put : x2 + 1/x2 = t
(2x - 2)/x3 .dx = dt
2(x4-1)x3.dx=dt
I = integral of { (x4-1)/x2*x(x2+1+(1/x2)) .dx }
= integral of { (1/2.(t)1/2 ).dt }
= 1/2 * 2*(t)1/2 + C
= (x2 + (1/x2) +1)1/2 + C
--
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