   Chapter 7.R, Problem 51E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0 ). ∫ ln ( x 2 + 2 x + 2 ) d x

To determine

To Find:ln(x2+2x+2)dx

Explanation

Formula Used: uvdx=uvdxu'(vdx)dx

Calculation:

Initially looking at the integrand, you don’t have any clue how to integrate. But there is one way which always can be applied to find integral. The method here we are going to apply is integration by parts. Apply this method by taking u=ln(x2+2x+1) and v=1 for the given integral.

ln(x2+2x+2)dx=ln(x2+2x+2)×1dx=ln(x2+2x+2)×x2x+2x2+2x+2×xdx

Now, rewrite the remaining integrand so that you it is a known integrable functions a shown below:

ln(x2+2x+2)dx=xln(x2

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