Answer the following True or False. int3^(x)dx=(3^(x)+C)/(ln 3) True False

Apply Exponential Function Formula: To solve the integral of 3^(x) with respect to x, we need to use the formula for integrating exponential functions, which is ∫a^(x)dx = (a^(x) / ln(a)) + C, where a is a constant and a ≠ 1.Calculate Integral of 3^(x): We apply the formula to 3^(x), where a = 3. So, ∫3^(x)dx = (3^(x) / ln(3)) + C.Compare Result with Given Expression: We compare the result with the given expression (3^(x) + C) / (ln 3). The integral we found, (3^(x) / ln(3)) + C, is not the same as (3^(x) + C) / (ln 3) because in the given expression, both 3^(x) and C are divided by ln(3), which is incorrect.Verify Statement: Therefore, the statement ＂int3^(x)dx = (3^(x) + C) / (ln 3)＂ is False because the correct integral of 3^(x) is (3^(x) / ln(3)) + C, not both terms divided by ln(3).

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Answer the following True or False. $\newline$ $\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}$ $\newline$ True $\newline$ False

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Q. Answer the following True or False.

\newline

\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}

\newline

True

\newline

False

Apply Exponential Function Formula: To solve the integral of $3^{x}$ with respect to $x$ , we need to 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 $a \neq 1$ .
Calculate Integral of $3^{x}$ : We apply the formula to $3^{x}$ , where $a = 3$ . So, $\int 3^{x}\,dx = \left(\frac{3^{x}}{\ln(3)}\right) + C$ .
Compare Result with Given Expression: We compare the result with the given expression $(3^{x} + C) / (\ln 3)$ . The integral we found, $(3^{x} / \ln(3)) + C$ , is not the same as $(3^{x} + C) / (\ln 3)$ because in the given expression, both $3^{x}$ and $C$ are divided by $\ln(3)$ , which is incorrect.
Verify Statement: Therefore, the statement ＂ $\int 3^{x}\,dx = \frac{3^{x} + C}{\ln 3}$ ＂ is False because the correct integral of $3^{x}$ is $\frac{3^{x}}{\ln(3)}$ + C, not both terms divided by $\ln(3)$ .