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integrate x^2/(x^2+1)*(x^2+4) dx

integrate x^2/(x^2+1)*(x^2+4) dx

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

I = x2/(x2+1)(x2+4) dx

let x2 = t then

x2/(x2+1)(x2+4) = t/(t+1)(t+4)

now using partial fraction

t/(t+1)(t+4) = A/(t+1) + B/(t+4) 

A,B = -1/3 , 4/3

t/(t+1)(t+4) = -1/3(t+1) + 4/3(t+4)

again replacing t by x2

I  = [-1/3(x2+1) + 4/3(x2+4) ]dx                                             [ 1/x2+a2 dx = tan-1(x/a)/a ]

I = [ -tan-1x]/3 + 2tan-1(x/2)/3 ] + C

approve my ans if u like

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