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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

If ∫ x x + 1 + e^ x dx = px + qln |x + 1 + e^ x | + c, where c is...

If ∫xx+1+exdx=px+qln∣x+1+ex∣+c,∫ \dfrac{x}{x + 1 + e^{x}}dx = px + qln \left|x + 1 + e^{x}\right| + c, where cc is the constant of integration, then p+qp + q is equal to

Options

  1. A00
  2. B11
  3. C22
  4. D33

Correct answer

A. 00

Step-by-step solution

∫(x+1+ex)−(ex+1)x+1+exdx=∫(1−(ex+1)x+1+ex)dx=x−ln⁡∣x+1+ex∣+c∫ \dfrac{\left(x + 1 + e^{x}\right) - \left(e^{x} + 1\right)}{x + 1 + e^{x}}dx = ∫ \left(1 - \left(e^{x} + 1\right)x + 1 + e^{x}\right)dx = x - \ln \left|x + 1 + e^{x}\right| + c

On comparing,

p=1,q=−1p = 1, q = - 1
Hence, p+q=0p + q = 0

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