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Evaluate the integral ∫ e^(3x) dx.
Evaluate the integral ∫ e^(3x) dx.
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Practice Questions
1 question
Q1
Evaluate the integral ∫ e^(3x) dx.
(1/3)e^(3x) + C
(1/3)e^(3x)
3e^(3x) + C
e^(3x) + C
Show Solution
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The integral of e^(kx) is (1/k)e^(kx). Here, k = 3, so ∫ e^(3x) dx = (1/3)e^(3x) + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the integral ∫ e^(3x) dx.
Solution:
The integral of e^(kx) is (1/k)e^(kx). Here, k = 3, so ∫ e^(3x) dx = (1/3)e^(3x) + C.
Steps: 6
Show Steps
Step 1: Identify the integral you need to evaluate, which is ∫ e^(3x) dx.
Step 2: Recognize that the integral of e^(kx) is (1/k)e^(kx), where k is a constant.
Step 3: In this case, k is 3 because we have e^(3x).
Step 4: Substitute k = 3 into the formula: (1/3)e^(3x).
Step 5: Don't forget to add the constant of integration, C, to your answer.
Step 6: Write the final answer: ∫ e^(3x) dx = (1/3)e^(3x) + C.
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