Chapter 8.1, Problem 44E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding an indefinite Integral In Exercises 15–46, find the indefinite integral. ∫ 1 ( x − 1 ) 4 x 2 − 8 x + 3   d x

To determine

To calculate: The indefinite integral 1(x1)4x28x+3dx.

Explanation

Given: âˆ«1(xâˆ’1)4x2âˆ’8x+3dx.

Formula used:

âˆ«1uu2âˆ’a2du=1aarcsecâ€‰|u|a+c

Calculation:

Consider the integral âˆ«1(xâˆ’1)4x2âˆ’8x+3dx.

âˆ«1(xâˆ’1)4x2âˆ’8x+3dx=âˆ«1(xâˆ’1)4(x2âˆ’2x+34)dx=âˆ«12(xâˆ’1)(x2âˆ’2x+34)dz

Add and subtract 1 in denominator:

âˆ«1(xâˆ’1)4x2âˆ’8x+3dx=12âˆ«1(xâˆ’1)x2âˆ’2x+1âˆ’1+34dz=12âˆ«1(xâˆ’1)(xâˆ’1)2âˆ’14

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