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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

∫ (2012)^ 2x 1 - (2012)^ 2x (2012)^ ^ -1 (2012)^x dx =

∫(2012)2x1−(2012)2x(2012)sin⁡−1(2012)xdx=\int \frac{(2012)^{2x}}{\sqrt{1 - (2012)^{2x}}} (2012)^{\sin^{-1}(2012)^x} dx =

Options

  1. A(log⁡2012e)2(2012)sin⁡−1(2012)x+C(\log_{2012} e)^2 (2012)^{\sin^{-1}(2012)^x} + C
  2. B(log⁡2012e)2(2012)x+sin⁡−1(2012)x+C(\log_{2012} e)^2 (2012)^{x+\sin^{-1}(2012)^x} + C
  3. C(log⁡2012e)2(2012)sin⁡−1(2012)x+C(\log_{2012} e)^2 (2012)^{\sin^{-1}(2012)^x} + C
  4. D(2012)sin⁡−1(2012)x(log⁡2012e)2+C\frac{(2012)^{\sin^{-1}(2012)^x}}{(\log_{2012} e)^2} + C *(Note: Options 'a' and 'c' are printed identically in the source material .)*

Correct answer

C. (log⁡2012e)2(2012)sin⁡−1(2012)x+C(\log_{2012} e)^2 (2012)^{\sin^{-1}(2012)^x} + C

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