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

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

MathematicsIndefinite IntegrationWBJEEWBJEE 2011

Options:

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

Solution:

1109 Upvotes Verified Answer

The correct answer is: \(2^x f(x)+C\)

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

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