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$\int e^{5x} \, dx$

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Power property of logarithms

Full solution

Q.

\int e^{5x} \, dx

Identify Integral: Identify the integral that needs to be solved. $\newline$ We need to find the integral of the function $e^{5x}$ with respect to $x$ .
Apply Integration Rule: Apply the basic integration rule for $e^{ax}$ . The integral of $e^{ax}$ with respect to $x$ is $(\frac{1}{a})e^{ax} + C$ , where $C$ is the constant of integration.
Calculate Integral: Calculate the integral of $e^{5x}$ using the rule from Step $2$ . $\newline$ In our case, $a = 5$ , so the integral of $e^{5x}$ with respect to $x$ is $(\frac{1}{5})e^{5x} + C$ .
Write Final Answer: Write down the final answer. $\newline$ The integral of $e^{5x}$ with respect to $x$ is $(\frac{1}{5})e^{5x} + C$ .

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