\( \int x^{4} \cdot \ln (x) d x \)
\(u´=x^4 \) → \(u=\frac{1}{5}*x^5 \)
\( v= \ln (x) \) → \( v´=\frac{1}{x} \)
\( \int x^{4} \cdot \ln (x) d x=\frac{1}{5}*x^5*ln(x)-\int\limits_{}^{} \frac{1}{5}*x^5*\frac{1}{x}*dx\)
\( \int x^{4} \cdot \ln (x) d x=\frac{1}{5}*x^5*ln(x)-\frac{1}{5}*\int\limits_{}^{} x^4*dx\)
Am Ende noch +C
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