   Chapter 8.4, Problem 40E

Chapter
Section
Textbook Problem

# Completing the Square In Exercises 33-36, complete the square and find the indefinite integral. ∫ x x 2 − 6 x + 5 d x

To determine

To calculate: The solution of the following indefinite integral xx26x+5dx..

Explanation

Given:

The indefinite integral xx26x+5dx.

Formula used:

The integration of tanxsecx is tanxsecxdx=secx+C.

The integration of secx is secxdx=ln|secx+tanx|+C.

Calculation:

Consider the following expression

x26x+5.

Simplify the above expression, to get;

x26x+5=x26x+94x26x+5=(x3)222

We get;

xx26x+5dx=x(x3)222dx …….(1)

Now, assume,

x3=2secθ

x3=2secθx=3+2secθ

Now differentiate above expression with respect to x;

dx=2secθtanθdθ

Substitute above value of x and dx in equation (1) and simplify,

x(x3)222dx=(2secθ+3)(2secθ)24(2secθtanθ)dθx(x3)222dx=

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