Question

`int_2^3 x/(x^2 - 1)` dx = ______

विकल्प

• `log(8/3)`

• `1/2log(8/3)`

• `log(3/8)`

• `1/2log(3/8)`

Answer 1

`int_2^3 x/(x^2 - 1)` dx = `underline(1/2log(8/3))`

Explanation:

`int_2^3 x/(x^2 - 1) dx = 1/2int_2^3 (2x)/(x^2 - 1) dx`

= `1/2[log|x^2 - 1|]_2^3` ......`[int(f^'(x))/f(x) = log|f(x)| + c]`

= `1/2(log8 - log3)`

= `1/2log(8/3)`