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GUJCET · Maths · Integrals
\(\int \frac{x+100}{(x+101)^2} e^x d x=\) __________ \(+C\).
- A \(\frac{1}{x+100} e^x\)
- B \(\frac{1}{x+101} e^x\)
- C \(\frac{1}{x-101} e^x\)
- D \((x+101) e^x\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{x+101} e^x\)
Step-by-step Solution
Detailed explanation
\( \int \frac{x+100}{(x+101)^2} e^x d x = \int \left( \frac{(x+101)-1}{(x+101)^2} \right) e^x d x \) \( = \int \left( \frac{1}{x+101} - \frac{1}{(x+101)^2} \right) e^x d x \)
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