AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^3-x^2+x-1}{x-1} d x\) is equal to
- A \(\frac{x^3}{3}-x+c\)
- B \(\frac{x^2}{3}+x+c\)
- C \(\frac{x^3}{3}+x+c\)
- D \(2 x+c\)
Answer & Solution
Correct Answer
(C) \(\frac{x^3}{3}+x+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} I & =\int \frac{x^3-x^2+x-1}{x-1} d x \\ & =\int \frac{x^2(x-1)+(x-1)}{(x-1)} d x=\int \frac{(x-1)\left(x^2+1\right)}{(x-1)} d x \\ I & =\int\left(x^2+1\right) d x \Rightarrow I=\frac{x^3}{3}+x+C\end{aligned}\)
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