COMEDK · Maths · 28. Indefinite Integration
\(\int x^{x}(1+\log x) d x=\)
- A \(x^{x}+C\)
- B \(x^{-x}+x\)
- C \(x \log x+x\)
- D \(\log x+x\)
Answer & Solution
Correct Answer
(A) \(x^{x}+C\)
Step-by-step Solution
Detailed explanation
We have, \(I=\int x^{x}(1+\log x) d x\) Let \(\quad x^{x}=t\) \(\Rightarrow \quad \frac{d t}{d x}=x^{x} \log x+x^{x}\) \(\Rightarrow \quad \frac{d t}{d x}=x^{x}(1+\log x)\) \(\Rightarrow \quad d t=x^{x}(1+\log x) d x\) Now, \(\quad I=\int d t\) \[ =t+C=x^{x}+C \]
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