   Chapter 13.5, Problem 28E ### 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 1-32. Identify the formula used. ∫ 0 3 x  In x 2 d x

To determine

To calculate: The value of integral 1exlnx2dx.

Explanation

Given Information:

The provided integral is 1exlnx2dx.

Formula used:

For any variable u, the integral formula is,

lnudu=u(lnu1)+C

Where, ‘a’ is not a function of u. and C is the constant of integration.

Differentiation of un with respect to u is nun1

The logarithmic property,

lne=1

The logarithmic property,

lnxn=nlnx

Calculation:

Consider the provided integral:

1exlnx2dx

Multiply and divide the integral by 2,

121elnx2(2xdx)

Let x2=t

Differentiate both the sides,

2xdx=dt

The limits now becomes,

When x=1,t=1

And when x=e,t=e2<

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