MHT CET · Maths · Indefinite Integration
\(\int e^x \frac{(x-1)}{(x+1)^3} \mathrm{~d} x=\)
- A \(\mathrm{e}^x(x+1)^2+\mathrm{c}, \quad\) where c is the constant of integration
- B \(\mathrm{e}^x(x+1)^3+\mathrm{c}\), where c is the constant of integration
- C \(\frac{\mathrm{e}^x}{(x+1)^2}+\mathrm{c}, \quad\) where c is the constant of integration
- D \(\frac{\mathrm{e}^x}{(x+1)^3}+\mathrm{c}, \quad\) where c is the constant of integration
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{e}^x}{(x+1)^2}+\mathrm{c}, \quad\) where c is the constant of integration
Step-by-step Solution
Detailed explanation
\(\int e^x \frac{(x-1)}{(x+1)^3} \mathrm{~d} x\) \( = \int e^x \left( \frac{(x+1)-2}{(x+1)^3} \right) \mathrm{~d} x\)
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