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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2010 · Mathematics · Indefinite Integration

What is ∫ e^ x x d x equal to? where c is a constant of integration.

What is ∫eln⁡xsin⁡xdx\int e^{\ln x} \sin x d x equal to? where cc is a constant of integration.

Options

  1. Aeln⁡x(sin⁡x−cos⁡x)+ce^{\ln x}(\sin x-\cos x)+\mathrm{c}
  2. B(sin⁡x−xcos⁡x)+c(\sin x-x \cos x)+\mathrm{c}
  3. C(xsin⁡x+cos⁡x)+c(x \sin x+\cos x)+\mathrm{c}
  4. D(sin⁡x+xcos⁡x)+c(\sin x+x \cos x)+\mathrm{c}

Correct answer

B. (sin⁡x−xcos⁡x)+c(\sin x-x \cos x)+\mathrm{c}

Step-by-step solution

The correct answer is option (B).
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