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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Indefinite Integration

BITSAT 2021 · Mathematics · Indefinite Integration

If ∫ (3 x+1)/((x-3)(x-5)) d x=∫ (-5)/((x-3)) d x+∫ (B)/((x-5)) d x...

If ∫3x+1(x−3)(x−5)dx=∫−5(x−3)dx+∫B(x−5)dx\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 BB is

Options

  1. A3
  2. B4
  3. C6
  4. D8

Correct answer

D. 8

Step-by-step solution

Wehave,We have,3x+1(x−3)(x−5)=−5x−3+Bx−53x+1=−5(x−5)+B(x−3) Put x=53(5)+1=B(5−3)16=2B or B=8\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}$$
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