JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \( f(x)=\int\frac{(2-x^{2})e^{x}}{(\sqrt{1+x})(1-x)^{\frac{3}{2}}}dx \). If \( f(0)=0 \), then \( f(\frac{1}{2}) \) is equal to:
- A \( \sqrt{3e}-1 \)
- B \( \sqrt{2e}+1 \)
- C \( \sqrt{2e}-1 \)
- D \( \sqrt{3e}+1 \)
Answer & Solution
Correct Answer
(A) \( \sqrt{3e}-1 \)
Step-by-step Solution
Detailed explanation
\( \int e^{x}\left(\frac{(1-x^{2})+1}{\sqrt{1+x}\cdot(1-x)^{3/2}}\right)dx \) \( \int e^{x}\left(\frac{(1-x^{2})}{\sqrt{1+x}\cdot(1-x)^{3/2}}+\frac{1}{\sqrt{1+x}\cdot(1-x)^{3/2}}\right)dx \)…
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