CBSE Class 12-science Answered
intigrate w.r.t x
Asked by sumahr | 20 Dec, 2009, 07:55: PM
Expert Answer
f(x) = (x3+x)/(x4-9) = x(x2+1)/[(x2-3)(x2+3)]
Put x2+1 = y, and xdx = dy/2
Hence f(x)dx = (x3+x)dx/(x4-9) = x(x2+1)dx/[(x2-3)(x2+3)]
= ydy/[2(y-4)(y+2)]
Partial fractionating,
= (dy/2)[2/(y-4) + 1/(y+2)]
(x3+x)dx/(x4-9) = (dy/2)[2/(y-4) + 1/(y+2)] = (1/2)[2log(y-4) + log(y+2)] + c
=(1/2)log [(x2-3)2(x2+3)] + c =log 
[(x2-3)2(x2+3)] + c
Regards,
Team,
TopperLearning.
Answered by | 20 Dec, 2009, 11:44: PM
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