   Chapter 13, Problem 25RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 23-26, using the formulas in Table 13.2. ∫ x  ln  x 2   d x

To determine

To calculate: The evaluation of the integral xlnx2dx.

Explanation

Given information:

The provided integral is,

xlnx2dx

Formula used:

Integration formula,

For the variable x and constant a which belongs to R, the integral of lnxdx is given by:

lnxdx=x(lnx1)+C

Calculation:

Consider the provided integral,

xlnx2dx

Above equation can be written as,

12lnx22xdx

Let u=x2

Differentiate above equation with respect to x,

dudx=2x

Thus,

du2x=dx

Now, substitute u as x2 and du2x for dx in above equation to get,

xlnx2dx=

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