`int(1)/(4x^(2)+4x+5)dx` का मान ज्ञात कीजिए ।

Explanation

`int(1)/(4x^(2)+4x+5)dx`
`=(1)/(4)int(1)/(x^(2)+x+(5)/(4))dx=(1)/(4)int(1)/((x^(2)+x+(1)/(4))+1)dx`
`=(1)/(4)int(1)/((x+(1)/(2))^(2)+1^(2))dx=(1)/(4).tan^(-1)((x+(1)/(2))/(1))+c`
`=(1)/(4)tan^(-1)((2x+1)/(2))+c`