JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int \limits_{1}^{2} e ^{ x } \cdot x ^{ x }\left(2+\log _{ e } x \right) d x\) equal
- A \(e (4 e +1)\)
- B \(e(2 e-1)\)
- C \(4 e^{2}-1\)
- D \(e (4 e -1)\)
Answer & Solution
Correct Answer
(D) \(e (4 e -1)\)
Step-by-step Solution
Detailed explanation
\(\int_{1}^{2} e ^{x} \cdot x ^{ x }\left(2+\log _{ e } x \right) d x\) \(\int_{1}^{2} e ^{ x }\left(2 x ^{ x }+ x ^{ x } \log _{ e } x \right) d x\) \(\int_{1}^{2} e ^{ x }(\frac{ x ^{ x }}{f( x )}+\underbrace{ x ^{ x }\left(1+\log _{ e } x \right)}_{f^{(}( x )}) d x\)…
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