TS EAMCET · Maths · Indefinite Integration
\(\int \frac{3-x^2}{1-2 x+x^2} e^x d x=e^x f(x)+c \Rightarrow f(x)\)
- A \(\frac{1+x}{1-x}\)
- B \(\frac{1-x}{1+x}\)
- C \(\frac{1+x}{x-1}\)
- D \(\frac{x-1}{1+x}\)
Answer & Solution
Correct Answer
(A) \(\frac{1+x}{1-x}\)
Step-by-step Solution
Detailed explanation
Given that, \(\int \frac{3-x^2}{1-2 x+x^2} e^x d x=e^x f(x)+c\) ...(i) Let \(\begin{aligned} I & =\int \frac{3-x^2}{1-2 x+x^2} e^x d x \\ & =\int \frac{3-x^2}{(1-x)^2} e^x d x \\ & =\int\left(\frac{2}{(1-x)^2}+\frac{1+x}{1-x}\right) e^x d x\end{aligned}\)…
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