`int(2x)/((x^(2)+1)(x^(2)+3))dx` का मान ज्ञात कीजिए ।

Explanation

माना `x^(2)=t rArr 2xdx=dt`
`therefore" "int(2x)/((x^(2)+1)x^(2)+3))dx=int(1)/((t+1)(t+3))dt` ltBrgt `=(1)/(2)int[(1)/((t+1))-(1)/((t+3))]dt`
`=(1)/(2)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`