Evaluate f 2x dx 2-1 Solution Steps Rewrite rational expression to exponential expression to make the function integrable. Find two functions within the integrand that forms a function-derivative pair to do so, we find an "inne function" with its derivative being multiplied outside of it. 3.) Next that we need is to have a simplified integrant, which is now all in terms of u, no x variables at all. = x² – 1, du : S(x? – 1) x 2xdx = 2xdx du n+1

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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What I have Learned
Fill the blank with the correct steps or solution.
2x
=dx
Evaluate f
Solution
Steps
Rewrite rational expression to exponential expression to
make the function integrable.
Find two functions within the integrand that forms a
function-derivative pair to do so, we find an "inner
function" with its derivative being multiplied outside of it.
3.)
Next that we need is to have a simplified integrant,
which is now all in terms of u, no x variables at all.
1.)
2.)
Let u = x2 - 1, du = 2xdx
S(x? – 1) x 2 xdx
du
4.)
Integrating by integral formula fu"du =
un+1
%3D
+ C.Then,
n+1
simplify the numerical coefficient.
The original equation never had a "u", the original question has x's.
5.)
To find the final answer, substitute u = x2- 1 .
%3D
Transcribed Image Text:What I have Learned Fill the blank with the correct steps or solution. 2x =dx Evaluate f Solution Steps Rewrite rational expression to exponential expression to make the function integrable. Find two functions within the integrand that forms a function-derivative pair to do so, we find an "inner function" with its derivative being multiplied outside of it. 3.) Next that we need is to have a simplified integrant, which is now all in terms of u, no x variables at all. 1.) 2.) Let u = x2 - 1, du = 2xdx S(x? – 1) x 2 xdx du 4.) Integrating by integral formula fu"du = un+1 %3D + C.Then, n+1 simplify the numerical coefficient. The original equation never had a "u", the original question has x's. 5.) To find the final answer, substitute u = x2- 1 . %3D
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