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GUJCET · Maths · Integrals
\(\int e^{\sqrt{x}} d x=\) __________ \(+c ; x > 0\)
- A \(2(\sqrt{x}-1) e^{\sqrt{x}}\)
- B \((1-\sqrt{x}) e^{\sqrt{x}}\)
- C \(2(1-\sqrt{x}) e^{\sqrt{x}}\)
- D \((\sqrt{x}-1) e^{\sqrt{x}}\)
Answer & Solution
Correct Answer
(A) \(2(\sqrt{x}-1) e^{\sqrt{x}}\)
Step-by-step Solution
Detailed explanation
Let \(u = \sqrt{x} \implies u^2 = x \implies 2u \, du = dx\) \(\int e^{\sqrt{x}} d x = \int e^u (2u \, du) = 2 \int u e^u \, du\)
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