CUET · MATHS · PYQ PAPER 2025
\(\int\left(e^{x \log a}+e^{a \log x}\right) d x\) is equal to (where \(\left.a>1\right)\)
- A \(\frac{a^x}{\log a}+\frac{x^{a+1}}{a+1}+C: C\) is an arbitrary constant
- B \((\log a) a^x+\frac{x^{a+1}}{a+1}+C: C\) is an arbitrary constant
- C \(\frac{a^x}{a+1}+\frac{x^{a+1}}{\log a}+C: C\) is an arbitrary constant
- D \((a+1) a^x+(\log a) x^{a+1}+C: C\) is an arbitrary constant
Answer & Solution
Correct Answer
(A) \(\frac{a^x}{\log a}+\frac{x^{a+1}}{a+1}+C: C\) is an arbitrary constant
Step-by-step Solution
Detailed explanation
\(\int\left(e^{x \log a}+e^{a \log x}\right) d x\) \(\int\left(e^{\log a^x}+e^{\log x^a}\right) d x\) \(\int\left(a^x+x^a\right) d x\) \(\frac{a^x}{\log a}+\frac{x^{a+1}}{a+1}+C\)
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