`int(dx)/(a^(2)+x^(2))` का मान ज्ञात कीजिए |

Explanation

माना `I=int(dx)/(a^(2)+x^(2))=(1)/(a^(2))int(dx)/(1+((x)/(a))^(2))`
माना `(x)/(a)=tan theta`
`therefore" "dx=a sec^(2) theta d theta`
`therefore" "I=(a)/(a^(2))int(sec^(2) theta d theta)/(1+tan^(2) theta)=(1)/(a) int d theta =(1)/(a) theta`
अतः `int(dx)/(a^(2)+x^(2))=(1)/(a) tan^(-1)((x)/(a))`
`" "[because tan theta =(x)/(a)rArr theta = tan^(-1)((x)/(a))]`