Lukas' Notes

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Indefinite Integral

2 min read

Examples
\int x^n (\log x)^n \ dx = \sum_{k=0}^n \frac{(-1)^k \cdot n!}{(n-k)! \cdot (n+1)^{k+1}} \cdot x^{n+1} \cdot (\log x)^{n-k}

Examples

Proof that the following equation holds for all via induction:

Start: Let , then:

Assumption:

Step:

q.e.d.

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