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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

∫ e^ x x + x ( (x^4 ^3 x - x x + x)/(x^2 ^2 x) ) dx =

∫exsin⁡x+cos⁡x(x4cos⁡3x−xsin⁡x+cos⁡xx2cos⁡2x)dx=\int e^{x\sin x + \cos x} \left( \frac{x^4 \cos^3 x - x\sin x + \cos x}{x^2 \cos^2 x} \right) dx =

Options

  1. Aexsin⁡x+cos⁡x(x−1cos⁡x)+Ce^{x\sin x + \cos x} \left( x - \frac{1}{\cos x} \right) + C
  2. Bexsin⁡x+cos⁡x(x−1xcos⁡x)+Ce^{x\sin x + \cos x} \left( x - \frac{1}{x\cos x} \right) + C
  3. Cexsin⁡x+cos⁡x(1−1xcos⁡x)+Ce^{x\sin x + \cos x} \left( 1 - \frac{1}{x\cos x} \right) + C
  4. Dexsin⁡x+cos⁡x(1−1cos⁡x)+Ce^{x\sin x + \cos x} \left( 1 - \frac{1}{\cos x} \right) + C

Correct answer

B. exsin⁡x+cos⁡x(x−1xcos⁡x)+Ce^{x\sin x + \cos x} \left( x - \frac{1}{x\cos x} \right) + C

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