Integrals of Exponential Functions

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Question 1 of 6

Find the integral

$\int e^{4x} dx$

1. $e^(4x)+c$
2. $4e^(4x)+c$
3. $1/4 e^x +c$
4. $1/4 e^(4x)+c$

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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

Find the integral

$\int e^{\frac{1}{2}x} dx$

1. $2e^(1/2x) +c$
2. $e^(1/2x) +c$
3. $1/2 e^(1/2x) +c$
4. $e^(4x) +c$

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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

$\int e^{\color{#004ec4}{a}x+b} dx$	$=$	$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$

$\int e^{\color{#004ec4}{\frac{1}{2}}x} dx$	$=$	$\frac{1}{\color{#004ec4}{\frac{1}{2}}} e^{\color{#004ec4}{\frac{1}{2}}x} +c$	Substitute known values

	$=$	$2e^(1/2x) +c$	Reciprocate the denominator

$2e^(1/2x) +c$

Question 3 of 6

Find the integral

$\int 12e^{3x} dx$

1. $4e^(x)+c$
2. $e^(4x)+c$
3. $12e^(3x)+c$
4. $4e^(3x)+c$

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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

$\int e^{\color{#004ec4}{a}x+b} dx$	$=$	$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$

$\int 12e^{\color{#004ec4}{3}x} dx$	$=$	$\frac{12}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x} +c$	Substitute known values

	$=$	$4e^(3x)+c$	Simplify

$4e^(3x)+c$

Question 4 of 6

Find the integral

$\int e^{2x-5} dx$

1. $1/2 e^(2x-5) +c$
2. $(2x-5)e^(2x-5) +c$
3. $2e^(2x-5) +c$
4. $e^(2x-5) +c$

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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

$\int e^{\color{#004ec4}{a}x+b} dx$	$=$	$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$

$\int e^{\color{#004ec4}{2}x-5} dx$	$=$	$\frac{1}{\color{#004ec4}{2}} e^{\color{#004ec4}{2}x-5} +c$	Substitute known values

$1/2 e^(2x-5) +c$

Question 5 of 6

Find the integral

$\int 6e^{3x+4} dx$

1. $(3x+4)e^(3x+4)+c$
2. $e^(3x)+c$
3. $e^(3x+4)+c$
4. $2e^(3x+4)+c$

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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

$\int e^{\color{#004ec4}{a}x+b} dx$	$=$	$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$

$\int 6e^{\color{#004ec4}{3}x+4} dx$	$=$	$\frac{6}{\color{#004ec4}{3}} e^{\color{#004ec4}{3}x+4} +c$	Substitute known values

	$=$	$2e^(3x+4)+c$	Simplify

$2e^(3x+4)+c$

Question 6 of 6

Find the integral

$\int \frac{1}{2} e^{5-3x} dx$

1. $-1/6 e^(5-3x)+c$
2. $e^(5-3x)+c$
3. $1/2 e^(5-3x)+c$
4. $1/6 e^(5-3x)+c$

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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

$\int e^{\color{#004ec4}{a}x+b} dx$	$=$	$\frac{1}{\color{#004ec4}{a}} e^{\color{#004ec4}{a}x+b} +c$

$\int \frac{1}{2}e^{5-\color{#004ec4}{3}x} dx$	$=$	$\frac{\frac{1}{2}}{\color{#004ec4}{-3}} e^{5-\color{#004ec4}{3}x} +c$	Substitute known values

	$=$	$-1/6 e^(5-3x)+c$	Simplify

$-1/6 e^(5-3x)+c$

Integrals of Exponential Functions

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Quiz summary

Information

1. Question

Hint

Great Work!

Integrating Exponential Functions with Base “e”

2. Question

Hint

Correct!

Integrating Exponential Functions with Base “e”

3. Question

Hint

Keep Going!

Integrating Exponential Functions with Base “e”

4. Question

Hint

Fantastic!

Integrating Exponential Functions with Base “e”

5. Question

Hint

Excellent!

Integrating Exponential Functions with Base “e”

6. Question

Hint

Nice Job!

Integrating Exponential Functions with Base “e”

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