Mathematics

Mathematics

Problem

∫xnlog⁡x dx=\int x^n \log x \, dx = (a) xn+1n+1{log⁡x+1n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x + \frac{1}{n+1} \right\} + c (b) xn+1n+1{log⁡x+2n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x + \frac{2}{n+1} \right\} + c (c) xn+1n+1{2log⁡x−1n+1}+c\frac{x^{n+1}}{n+1} \left\{ 2 \log x - \frac{1}{n+1} \right\} + c (d) xn+1n+1{log⁡x−1n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x - \frac{1}{n+1} \right\} + c (a) xn+1n+1{log⁡x+1n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x + \frac{1}{n+1} \right\} + c (b) xn+1n+1{log⁡x+2n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x + \frac{2}{n+1} \right\} + c (c) xn+1n+1{2log⁡x−1n+1}+c\frac{x^{n+1}}{n+1} \left\{ 2 \log x - \frac{1}{n+1} \right\} + c (d) xn+1n+1{log⁡x−1n+1}+c\frac{x^{n+1}}{n+1} \left\{ \log x - \frac{1}{n+1} \right\} + c

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