What method is chosen to evaluate the integral of the natural log of 2x?

Integration by Parts with Natural Logarithms

Interactive Video
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Mathematics, English, Science
•
10th - 12th Grade
•
Hard

Mia Campbell
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Partial fraction decomposition
Trigonometric substitution
Integration by parts
Integration by substitution
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the natural log function chosen as u in integration by parts?
Because it is easy to differentiate
Because it is easy to integrate
Because it is a constant function
Because it simplifies the integral
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the natural log of 2x?
1/(2x)
2/(2x)
1/x
2/x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integral of dv when dv is equal to dx?
ln(x)
x
2x
1/x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of applying the chain rule in this integration?
To find the constant of integration
To integrate the natural log function
To differentiate the natural log function
To simplify the integral
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating x times 1/x?
0
1
ln(x)
x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final antiderivative of the integral of the natural log of 2x?
x ln(2x) + C
x ln(2x) - x + C
ln(2x) - x + C
x ln(x) - x + C
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