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Antiderivatives of Exponential FunctionsAntiderivatives of Exponential Functions
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Question 1 of 6
1. Question
Find the integral$$\int e^{4x} dx$$Hint
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Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{4}x} dx$$ `=` $$\frac{1}{\color{#004ec4}{4}} e^{\color{#004ec4}{4}x} +c$$ Substitute known values `1/4 e^(4x)+c` -
Question 2 of 6
2. Question
Find the integral$$\int e^{\frac{1}{2}x} dx$$Hint
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Correct!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{\frac{1}{2}}x} dx$$ `=` $$\frac{1}{\color{#004ec4}{\frac{1}{2}}} e^{\color{#004ec4}{\frac{1}{2}}x} +c$$ Substitute known values `=` `2e^(1/2x) +c` Reciprocate the denominator `2e^(1/2x) +c` -
Question 3 of 6
3. Question
Find the integral$$\int 12e^{3x} dx$$Hint
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Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int 12e^{\color{#004ec4}{3}x} dx$$ `=` $$\frac{12}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x} +c$$ Substitute known values `=` `4e^(3x)+c` Simplify `4e^(3x)+c` -
Question 4 of 6
4. Question
Find the integral$$\int e^{2x-5} dx$$Hint
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Fantastic!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int e^{\color{#004ec4}{2}x-5} dx$$ `=` $$\frac{1}{\color{#004ec4}{2}} e^{\color{#004ec4}{2}x-5} +c$$ Substitute known values `1/2 e^(2x-5) +c` -
Question 5 of 6
5. Question
Find the integral$$\int 6e^{3x+4} dx$$Hint
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Excellent!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int 6e^{\color{#004ec4}{3}x+4} dx$$ `=` $$\frac{6}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x+4} +c$$ Substitute known values `=` `2e^(3x+4)+c` Simplify `2e^(3x+4)+c` -
Question 6 of 6
6. Question
Find the integral$$\int \frac{1}{2} e^{5-3x} dx$$Hint
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Nice Job!
Incorrect
Integrating Exponential Functions with Base “e”
$$\int e^{\color{#004ec4}{a}x+b} dx=\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$Substitute the components into the formula$$\int e^{\color{#004ec4}{a}x+b} dx$$ `=` $$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$$ $$\int \frac{1}{2}e^{5-\color{#004ec4}{3}x} dx$$ `=` $$\frac{\frac{1}{2}}{\color{#004ec4}{-3}} e^{5-\color{#004ec4}{3}x} +c$$ Substitute known values `=` `-1/6 e^(5-3x)+c` Simplify `-1/6 e^(5-3x)+c`
Quizzes
- Antiderivatives (Indefinite Integrals) 1
- Antiderivatives (Indefinite Integrals) 2
- Antiderivatives (Indefinite Integrals) 3
- Antiderivatives of Exponential Functions
- Antiderivatives of Logarithmic Functions 1
- Antiderivatives of Logarithmic Functions 2
- Antiderivatives of Trig Functions 1
- Antiderivatives of Trig Functions 2
- Definite Integrals
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions