Indefinite Integrals

Question

The integral ∫(1/x) dx equals

RankGuru · Accepted Answer

1. **Standard Result**: The power rule formula $\frac{x^{n+1}}{n+1}$ fails for $n = -1$ (division by zero).
2. **Logarithmic Answer**: The derivative of $\ln(x)$ is $1/x$. 
3. **Absolute Value**: Because $1/x$ is defined for negative $x$ (where $\ln x$ is not), we must include an absolute value to cover the entire domain of $1/x$.
4. **Result**: $\int \frac{1}{x} \, dx = \ln|x| + C$.

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Indefinite Integrals

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Indefinite Integrals

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Evaluate $\int e^{x} (\frac{1 + x l n x}{x}) d x$ (Assume $x > 0$ and base $e$ for $ln$ ).