`int (dx)/sqrt(x^(2)-9)` का मान ज्ञात कीजिए?

Options

A. `log |x+9|+c`
B. `log |x+sqrt(x^(2))|+c`
C. `log |x+sqrt(x^(2)-9)|+c`
D. `log |x-9|+c`

Answer

C

Explanation

प्रथम विधि: `int (1)/sqrt(x^(2)-9) dx = int (dx)/sqrt((x)^(2)-(3)^(2))`
`=log |x+sqrt(x^(2)-9)|+c`
द्वितीय विधि : मानलो `x=3 sec theta implies dx=3 sec theta tan theta d theta`
अतः समाकल `=int (3 sec theta tan theta d theta)/sqrt(9 sec^(2) theta-9)= int (3 sec theta. Tan theta d theta)/(3 tan theta)`
`=int sec theta d theta=log |sec theta + tan theta|+c`
`=log |x+sqrt(x^(2)-9)|+c`.