समाकलन ज्ञात करें `int (dx)/(9x^2 +6x+5)`

Options

A. `1/(6)tan^(-1)((3x+1)/2)+c`
B. `1/(3)tan^(-1)((3x+1)/2)+c`
C. `1/(2)tan^(-1)((x+1)/2)+c`
D. इनमे से कोई नहीं

Answer

A

Explanation

`9x^2 + 6x +5 =9 (x^2 +2/3x) +5`
`=9(x^2+2x""1/3+1/9-1/9)+5=9(x+1/3)^2+4`
`=9(x+1/3)^2 +2^2 = (3x+1)^2 +2^2`
अब, `I =int (dx)/((3x+1)^2+2^2)`
`=1/(3xx2)tan^(-1)((3x+1)/2)+c" "[because int (dx)/(x^2 +a^2)=1/a tan^(-1) (x/a)]`