
Integrating Rational Functions and Substitutions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Lucas Foster
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial step taken to simplify the integral of (4x + 5) / (x^2 + 4)?
Split into two separate integrals
Apply integration by parts
Factor out the constants
Use partial fraction decomposition
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When factoring out constants from the integrals, what substitution is suggested for the first integral?
u = 2x
u = x
u = 4x + 5
u = x^2 + 4
Tags
CCSS.HSF.TF.C.8
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the differential du in terms of dx for the substitution u = x?
du = x dx
du = 1/2 dx
du = 2x dx
du = dx
Tags
CCSS.HSF.TF.C.8
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What form does the second integral take, which involves a^2 + u^2?
u^2 + a^2
1/(a^2 + u^2) du
1/u du
1/(u^2 - a^2) du
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of 'a' in the second integral form a^2 + u^2?
3
2
1
4
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which function is used to integrate the first part of the expression after substitution?
Exponential function
Natural logarithm
Sine function
Cosine function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical function is used to integrate the second part of the expression?
Arcsine
Arccotangent
Arctangent
Arccosine
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