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Questions and Answers
What is the integral of $5^x$ with respect to x?
What is the integral of $5^x$ with respect to x?
- $5^{x+1} + C$
- $5^x$
- $\frac{5^x}{\ln(5)}$
- $\frac{5^x}{\ln(5)} + C$ (correct)
What is the antiderivative of $5^x$?
What is the antiderivative of $5^x$?
- $5^x$
- $\frac{5^x}{\ln(5)}$
- $\frac{5^x}{\ln(5)} + C$ (correct)
- $5^{x+1} + C$
What is the indefinite integral of $5^x$?
What is the indefinite integral of $5^x$?
- $5^x$
- $\frac{5^x}{\ln(5)}$
- $5^{x+1} + C$
- $\frac{5^x}{\ln(5)} + C$ (correct)
What is the integral of an exponential function $a^x$?
What is the integral of an exponential function $a^x$?
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Study Notes
Exponential Functions Integration
- The integral of $5^x$ with respect to x is $\frac{5^x}{\ln 5} + C$, where $C$ is the constant of integration.
- The antiderivative of $5^x$ is $\frac{5^x}{\ln 5} + C$, which is a general form of the integral.
- The indefinite integral of $5^x$ is also $\frac{5^x}{\ln 5} + C$, emphasizing the non-specific limits of integration.
- The integral of an exponential function $a^x$ is $\frac{a^x}{\ln a} + C$, where $a$ is a positive real number and $a \neq 1$.
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