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Evaluate : int(2x)/((x^2+1)\ (x^2+3))\ d...

Evaluate : `int(2x)/((x^2+1)\ (x^2+3))\ dx`

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`" Let " int (2x)/((x^(2)+1)(x^(2)+3))dx`
` " Let " x^(2)=t rArr 2x dx=dt `
` :. I= int (1dt)/((t+1)(t+3))= int (1)/((t+1)(t+3))dx`
`" Let " (1)/((t+1)(t+3)) =(A)/(t+1)+(B)/(t+3)`
`rArr (1)/((t+1)(t+3)) =(A(t+3)+B(t+1))/((t+1)(t+3))`
`rArr 1=A (t+3) +B(t+1)`
` t=-1 then =0 + B(-3+1) rArr B =- (1)/(2)`
`:. I= (1)/(3) int(1)/(t+1) dt-(1)/(2) int(1)/(t+3) dt`
`=(1)/(2) log |t+1|-(1)/(2) log |t+3|+c`
`=(1)/(2) log |(t+1)/(t+3)| + C =(1)/(2)log |(x^(2)+1)/(x^(2)+3)|+c`
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