`int (dx)/(3x^(2)+13 x-10)` का मान ज्ञात कीजिए।

Answer

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Explanation

`int (dx)/(3x^(2)+13 x-10)=1/3 int (dx)/(x^(2)+(13x)/3-10/3)`
`=1/3 int (dx)/((x+13/6)^(2)-(17/6)^(2))`
अब माना `x+13/6=t`, तब `dx=dt`
`=1/3 int (dt)/(t^(2)-(17/6)^(2))`
`=(1)/(3xx2xx17/6) log |(t-17/6)/(t+17/6)|+c_(1)`
`=1/17 log |(x+13/6-17/6)/(x+13/6+17/6)|+c_(1)`
`=1/17 log |(6x-4)/(6x+30)|+c_(1)`
`=1/17 log |(2(3x-2))/(6(x+5))|+c_(1)`
`=1/17 log |((3x-2))/(3(x+5))|+c_(1)`
`=1/17 log |(3x-2)/(x+5)|+1/17 "log" 1/3 +c_(1)`
`=1/17 log |(3x-2)/(x+5)|+c`, जहाँ `c=c_(1)+1/17 "log" 1/3`