Mathematics

Evaluate:
$$\displaystyle\int x^n\log_ex\ dx$$


SOLUTION
Now,
$$\displaystyle\int x^n\log_ex\ dx$$
$$=\log_ex .\dfrac{x^{n+1}}{n+1}$$$$-\displaystyle\int \dfrac{1}{x}\dfrac{x^{n+1}}{n+1}\ dx$$
$$=\log_ex .\dfrac{x^{n+1}}{n+1}$$$$-\dfrac{x^{n+1}}{(n+1)^2}\ +c $$ [ Where $$c$$ being integrating constant]
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Subjective Medium Published on 17th 09, 2020
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