Class CBSE Class 12 Mathematics Integrals Q #805
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
8. $\int e^{5\log x}dx$ is equal to :
(A) $\frac{x^{5}}{5}+C$
(B) $\frac{x^{6}}{6}+C$
(C) $5x^{4}+C$
(D) $6x^{5}+C$
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AI Tutor Explanation

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Step-by-Step Solution

  1. Simplify the expression using logarithm properties:

    \( e^{5\log x} = e^{\log x^5} = x^5 \)

  2. Integrate the simplified expression:

    \( \int x^5 dx = \frac{x^{5+1}}{5+1} + C = \frac{x^6}{6} + C \)

Correct Answer: \(\frac{x^{6}}{6}+C\)

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the properties of logarithms and integration to solve the problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure involving logarithmic simplification and then integration.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of integration techniques and logarithmic properties as covered in the textbook.

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