Write a value

Question:

Write a value of $\int a^{x} e^{x} d x$

Solution:

We know that a and e are constant so, $a^{x} e^{x}=(a e)^{x}$

$y=\int(a e)^{x} d x$

Use formula $\int c^{x}=\frac{c^{x}}{\log c}$ where $c$ is constant

$y=\frac{(a e)^{x}}{\log (a e)}+c$

$y=\frac{a^{x} e^{x}}{\log a+1}+c$

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