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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Indefinite Integration

BITSAT 2011 · Mathematics · Indefinite Integration

Evaluate (∫ (x^2)/(x^2-1) d x)

Evaluate (\int \frac{x^2}{x^2-1} d x)

Options

  1. A(x-\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c})
  2. B(x+\frac{1}{2} \log \left(\frac{x+1}{x-1}\right)+c)
  3. C(x+\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c})
  4. DNone of these

Correct answer

C. (x+\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c})

Step-by-step solution

Given integral (I=\int\left(1+\frac{1}{x^2-1}\right) d x) (=∫dx+∫dx(x−1)(x+1)=x+12∫(1x−1−1x+1)dx=x+12log⁡(x−1x+1)+c\begin{aligned} & =\int d x+\int \frac{d x}{(x-1)(x+1)} \\ & =x+\frac{1}{2} \int\left(\frac{1}{x-1}-\frac{1}{x+1}\right) d x=x+\frac{1}{2} \log \left(\frac{x-1}{x+1}\right)+c \end{aligned})
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