Question

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

• A. 3
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (D)

We have,
$\frac{3x+1}{\left(x-3\right)\left(x-5\right)}=\frac{-5}{x-3}+\frac{B}{x-5}$
$3x+1=-5\left(x-5\right)+B\left(x-3\right)$
Put $x=5$
$3\left(5\right)+1=B\left(5-3\right)$
$16=2B$ or $B=8$