Indefinite Integrals

Identify Rule: Apply the Power Rule for integration, which states $\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C$ for $n \neq = - 1$ .
Substitution: Here $n = 2$ .
Calculation:
- $\int x^{2} d x = \frac{x ^{2 + 1}}{2 + 1} + C$
- $= \frac{x ^{3}}{3} + C$ .
Constant of Integration: The constant $C$ is added because differentiation of any constant is zero, making it an indefinite integral.

This easy difficulty mathematics question is from the chapter integral calculus, covering the topic of indefinite integrals. It appeared in the 2025 exam.

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Indefinite Integrals

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Solution

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