COMEDK · Maths · 28. Indefinite Integration
\(\int x^x(1+\log x) d x\) is equal to
- A \(x^x+c\)
- B \(x \log x+c\)
- C \(x^{x-1}+c\)
- D \(x^x \log x+c\)
Answer & Solution
Correct Answer
(A) \(x^x+c\)
Step-by-step Solution
Detailed explanation
Let \(I = \int x^x(1 + \log x) dx\). Consider the function \(f(x) = x^x\). To differentiate \(f(x)\), take the natural logarithm on both sides: \(\ln(f(x)) = \ln(x^x) = x \ln x\). Differentiating both sides with respect to \(x\):…
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