MHT CET · Maths · Indefinite Integration
\(\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=\)
- A \(\frac{x^2}{2}+3 x-\log |x|+\mathrm{c}\), where c is a constant of integration.
- B \(\frac{x^2}{2}+3 x+2 \log |x|+\mathrm{c}\), where c is a constant of integration.
- C \(\frac{x^2}{2}-3 x+2 \log |x|+\mathrm{c}\), where c is a constant of integration.
- D \(\frac{x^2}{2}-3 x-\log |x|+\mathrm{c}\), where c is a constant of integration.
Answer & Solution
Correct Answer
(C) \(\frac{x^2}{2}-3 x+2 \log |x|+\mathrm{c}\), where c is a constant of integration.
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text {Let I } & =\int \frac{x^3-7 x+6}{x^2+3 x} \\ & =\int\left(x-3+\frac{2 x+6}{x^2+3 x}\right) \mathrm{d} x \\ & =\int\left(x-3+\frac{2(x+3)}{x(x+3)}\right) \mathrm{d} x \\ & =\int\left(x-3+\frac{2}{x}\right) \mathrm{d} x \\ & =\frac{x^2}{2}-3 x+2 \log |x|+\mathrm{c}\end{aligned}\)
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