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In this question, you will use a substitution to carry out the following integration: So If the answer requires a constant of integration, enter it as c. 8 (x³ +2) ³ (x³ +2)8 5x¹ dx a. The integral involves the composite function u = g(x) = du b. Find the derivative dx : du dx = c. Transform the original integral into one involving u by using the substitution rule: • Replace all occurrences of 9 (x) in the integral by U. du What u-substitution will simplify this term? '(x) dx by du (equivalently: replace o Replace 9 [ (x³ +2)³ 5x¹ dx = du dx text( )(du)/(dx) dx (you do not need to enter du in your answer) d. Carry out the integration, and find the most general antiderivative (in terms of u). antiderivative : e. Finally, rewrite your answer in terms of x by replacing u by g(x). 8 4 [ (x³ + 2)³ 5x¹ da = ✪

In this question, you will use a substitution to carry out the following integration: So If the answer requires a constant of integration, enter it as c. 8 (x³ +2) ³ (x³ +2)8 5x¹ dx a. The integral involves the composite function u = g(x) = du b. Find the derivative dx : du dx = c. Transform the original integral into one involving u by using the substitution rule: • Replace all occurrences of 9 (x) in the integral by U. du What u-substitution will simplify this term? '(x) dx by du (equivalently: replace o Replace 9 [ (x³ +2)³ 5x¹ dx = du dx text( )(du)/(dx) dx (you do not need to enter du in your answer) d. Carry out the integration, and find the most general antiderivative (in terms of u). antiderivative : e. Finally, rewrite your answer in terms of x by replacing u by g(x). 8 4 [ (x³ + 2)³ 5x¹ da = ✪

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter5: Polynomial And Rational Functions
Section: Chapter Questions
Problem 26PT: Find the unknown value. y varies inversely as the square of x and when x=3,y=2. Find y if x=1.
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In this question, you will use a substitution to carry out the following integration: [ (x³ + 2)³ 5x¹ da dx If the answer requires a constant of integration, enter it as c. 8 a. The integral involves the composite function (x³ + 2) What u-substitution will simplify this term? U = g(x) = du b. Find the derivative dx : du dx = c. Transform the original integral into one involving u by using the substitution rule: • Replace all occurrences of 9 (x) in the integral by U. du =dx g'(x) dx by du (equivalently: replace J o Replace S (x5 +2)8 5x¹ dx du text()(du)/(dx) dx (you do not need to enter du in your answer) d. Carry out the integration, and find the most general antiderivative (in terms of u). antiderivative : e. Finally, rewrite your answer in terms of x by replacing u by g(x). [ (x³ + 2)³ 5x¹ dx
Transcribed Image Text:In this question, you will use a substitution to carry out the following integration: [ (x³ + 2)³ 5x¹ da dx If the answer requires a constant of integration, enter it as c. 8 a. The integral involves the composite function (x³ + 2) What u-substitution will simplify this term? U = g(x) = du b. Find the derivative dx : du dx = c. Transform the original integral into one involving u by using the substitution rule: • Replace all occurrences of 9 (x) in the integral by U. du =dx g'(x) dx by du (equivalently: replace J o Replace S (x5 +2)8 5x¹ dx du text()(du)/(dx) dx (you do not need to enter du in your answer) d. Carry out the integration, and find the most general antiderivative (in terms of u). antiderivative : e. Finally, rewrite your answer in terms of x by replacing u by g(x). [ (x³ + 2)³ 5x¹ dx
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