AP EAMCET · Maths · Indefinite Integration
\(\int 3^x\left(f^{\prime}(x)+f(x) \log 3\right) d x\) is equal to
- A \(3^x f^{\prime}(x)+c\)
- B \(3^x \log 3+c\)
- C \(3^x f(x)+c\)
- D \(3^x+c\)
Answer & Solution
Correct Answer
(C) \(3^x f(x)+c\)
Step-by-step Solution
Detailed explanation
Let \(\left.I=\int 3^x f^{\prime}(x)+f(x) \log 3\right) d x\) \(I=\int 3^x f^{\prime}(x) d x+\int 3^x f(x) \log 3 d x\) \(\begin{aligned} & I=3^x f(x)-\int\left(3^x f(x) \log 3\right) d x+\int 3^x f(x) \log 3 d x \\ & I=3^x f(x)+c\end{aligned}\)
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