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Answer the following True or False. $\newline$ $\int 8^x \, dx = \frac{8^x + C}{\ln 8}$ $\newline$ True $\newline$ False

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Properties of matrices

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Q. Answer the following True or False.

\newline

\int 8^x \, dx = \frac{8^x + C}{\ln 8}

\newline

True

\newline

False

Apply Exponential Formula: To solve the integral of $8^x$ with respect to $x$ , we use the formula for integrating exponential functions, which is $\int a^x dx = \frac{a^x}{\ln a} + C$ , where $a$ is a constant and $C$ is the constant of integration.
Calculate Integral: We apply the formula to $8^x$ . Here, $a$ is $8$ , so we have $\int 8^x \, dx = \frac{8^x}{\ln 8} + C$ .
Compare with Given Expression: We compare the result with the given expression $(8^{x}+C)/(\ln 8)$ . The given expression is not correct because it has the entire term $(8^x + C)$ divided by $\ln(8)$ , which is not the same as the correct integral result $(8^x)/(\ln 8) + C$ .
Verify Statement: Therefore, the statement ＂ $\int 8^x \, dx = \frac{8^x + C}{\ln 8}$ ＂ is False because the correct integral of $8^x$ is $\frac{8^x}{\ln 8} + C$ , not $\frac{8^x + C}{\ln 8}$ .

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