AP EAMCET · Maths · Indefinite Integration
If \(\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=f(x)+\) arbitrary constant, then \(f(x)=\)
- A \(\frac{x e^x}{x+4}\)
- B \(\frac{e^x}{x+4}\)
- C \(\frac{x e^x}{(x+4)^2}\)
- D \(\frac{e^x}{(x+4)^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{x e^x}{x+4}\)
Step-by-step Solution
Detailed explanation
Given, \(\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=f(x)+\mathcal{c}\) Now, \[ \begin{aligned} & \int e^x\left(\frac{x+2}{x+4}\right)^2 d x=\int e^x\left(\frac{x^2+4+4 x}{(x+4)^2}\right) d x \\ & =\int e^x\left(\frac{x}{x+4}+\frac{4}{(x+4)^2}\right) d x \end{aligned} \]…
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