Q111 / 160 · WBJEE 2011 · Mathematics

\(\int 2^x\left(f^{\prime}(x)+f(x) \log 2\right) d x\) is

  • A
    \(2^x \mathrm{f}^{\prime}(\mathrm{x})+\mathrm{C}\)
  • Correct answer
    B
    \(2^x f(x)+C\)
  • C
    \(2^x(\log 2) f(x)+C\)
  • D
    \((\log 2) f(x)+C\)

Solution

Hints: \(I=\int 2^x f^{\prime}(x) d x+\int 2^x f(x) \log 2 d x\) \(=2^x f(x)\)

Hence, the correct answer is option: 'B'.

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