Mathematics

Evaluate: $$\int \left( e ^ { a \log x } + e ^ { x \log a } \right) d x $$ 


ANSWER

$$\dfrac { x ^ { a + 1 } } { a + 1 } + \dfrac { a ^ { x } } { \log a } + c$$


SOLUTION
$$\displaystyle\int e^{alog x}+e^{xlog a}dx$$
$$=\displaystyle\int e^{log x^a}+e^{log a^x}dx$$
$$=\displaystyle\int x^a+a^xdx$$
$$=\dfrac{x^{a+1}}{a+1}+\dfrac{a^x}{log a}+c$$.
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Single Correct Medium Published on 17th 09, 2020
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