1 In section 7.5 from the textbook, please find a total of 4 integrals that you will apply the technique to evaluate:1) section 7.1: Integration by Parts2) section 7.2: Trigonometric Functions3) section 7.3: Trig Sub4) section 7.4: Partial FractionYou will need to solve it completely with the technique.Xa. dzdx1+x²1b. /__dzdx1 + x²· Sz√/2² - 1dz11 de1-x²

Answered: In section 7.5 from the textbook,…

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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Question

In section 7.5 from the textbook, please find a total of 4 integrals that you will apply the technique to evaluate:
1) section 7.1: Integration by Parts
2) section 7.2: Trigonometric Functions
3) section 7.3: Trig Sub
4) section 7.4: Partial Fraction
You will need to solve it completely with the technique.
X
a. dz
dx
1+x²
1
b. /__dz
dx
1 + x²
· Sz√/2² - 1dz
1
1 de
1-x²

Expert Solution

Step 1: Part (a) Integral for integration by parts:

“Since you have posted a question with multiple sub parts, we will provide the solution only to the first three sub parts as per our Q&A guidelines. Please repost the remaining sub parts separately.”

The third integral can be solved using integral by parts.

$I space equals space integral x square root of x squared space minus space 1 end root d x I space equals space x integral square root of x squared space minus space 1 end root d x space minus space integral left curly bracket fraction numerator d over denominator d x end fraction left parenthesis x right parenthesis space cross times space integral square root of x squared space minus space 1 end root d x right curly bracket d x I space equals space 2 over 3 x left parenthesis x squared space minus space 1 right parenthesis to the power of 3 divided by 2 end exponent space space minus space integral left parenthesis x squared space minus space 1 right parenthesis to the power of 3 divided by 2 end exponent d x I space equals space 2 over 3 x left parenthesis x squared space minus space 1 right parenthesis to the power of 3 divided by 2 end exponent space minus space 2 over 5 x left parenthesis x squared space minus space 1 right parenthesis to the power of 5 divided by 2 end exponent space plus thin space C$