   Chapter 8.6, Problem 17E

Chapter
Section
Textbook Problem

# Finding an Indefinite Integral In Exercises 19-40, use a table of integrals to find the indefinite integral. ∫ x   arcc s c ( x 2 + 1 )   d x

To determine

To calculate: The value of the indefinite integral xarccsc(x2+1)dx using the table of integrals.

Explanation

Given: We are given with the Indefinite integral expression xarccsc(x2+1)dx.

Formula used:

We will use formula 80 from the table of integrals:arccscudu=uarccscu+ln|u+u21|+C

Calculation:

Compare the form of given Indefinite Integral with Formula 80 involving inverse trigonometric functions:

arccscudu=uarccscu+ln|u+u21|+C

We assume that u=x2+1.

Then du=2xdx, thus we get that:

xarccsc(x2+1)dx=12arccsc(

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