Q85 / 125 · BITSAT 2021 · Mathematics

If $\int \frac{3 x+1}{(x-3)(x-5)} d x=\int \frac{-5}{(x-3)} d x+\int \frac{B}{(x-5)} d x$ then the value of $B$ is

  • A
    3
  • B
    4
  • C
    6
  • Correct answer
    D
    8

Solution

We have, $\begin{array}{l} \frac{3 x+1}{(x-3)(x-5)}=\frac{-5}{x-3}+\frac{\mathrm{B}}{x-5} \\ 3 x+1=-5(x-5)+\mathrm{B}(x-3) \\ \text { Put } x=5 \\ 3(5)+1=\mathrm{B}(5-3) \\ 16=2 \mathrm{~B} \text { or } \mathrm{B}=8 \end{array}$

Hence, the correct answer is option: 'D'.

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