I need help to understand substitution with homework question. Ty!

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need help to understand substitution with homework question. Ty!
the quvern
Evaluate the following indefinte by uong
facax+6)dx u= ax+6
substitution t pedue
the integral to
standand lenm.
du - x> du= x² dx
dx
thus
2x dx
Transcribed Image Text:the quvern Evaluate the following indefinte by uong facax+6)dx u= ax+6 substitution t pedue the integral to standand lenm. du - x> du= x² dx dx thus 2x dx
Expert Solution
Step 1

The given integral is I=22x+68dx.

The integral is solved using substitution method.

Consider u=2x+6.

Step 2

Let 2x+6=u

Now, differentiate both sides.

2dx=du

Substitute u for 2x+6 and du for 2dx in the given integral I=22x+68dx.

I=u8du =u99+C                    1

where C is the constant of integration.

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