Mathematics

Evaluate the following integral:
$$\displaystyle\int{{e}^{a\log_{e}{x}}dx},\,\,a>0,a\neq\,1$$


SOLUTION
$$\displaystyle\int{{e}^{a\log_{e}{x}}dx},\,\,a>0,a\neq\,1$$

$$=\displaystyle\int{{e}^{\log_{e}{{x}^{a}}}dx}$$ since $${a}^{\log_{a}{N}}=N$$

$$=\displaystyle\int{{x}^{a}\,dx}$$

$$=\dfrac{1}{a+1}{x}^{a+1}+c$$ since $$\displaystyle\int{{x}^{n}\,dx}=\dfrac{{x}^{n+1}}{n+1}+c$$
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Subjective Medium Published on 17th 09, 2020
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