MHT CET · Maths · Indefinite Integration
\(\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x\) is
- A \(\frac{\mathrm{e}^x}{(x+6)^2}+\mathrm{c}\), where c is the constant of integration.
- B \(\frac{e^x}{x+5}+c,\) where \(c\) is the constant of integration.
- C \(\frac{\mathrm{e}^x}{(x+5)^2}+\mathrm{c}\), where c is the constant of integration.
- D \(\frac{\mathrm{e}^x}{x+6}+\mathrm{c},\) where c is the constant of integration.
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{e}^x}{x+6}+\mathrm{c},\) where c is the constant of integration.
Step-by-step Solution
Detailed explanation
\(\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x = \int \mathrm{e}^x\left(\frac{(x+6)-1}{(x+6)^2}\right) \mathrm{d} x\) \(= \int \mathrm{e}^x\left(\frac{1}{x+6} - \frac{1}{(x+6)^2}\right) \mathrm{d} x\)
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