   Chapter 13.5, Problem 25E ### 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. ∫ d x ( 3 x + 1 ) 2 + 1

To determine

To calculate: The value of integral dx(3x+1)2+1.

Explanation

Given Information:

The provided integral is dx(3x+1)2+1.

Formula used:

For any variable u, the integral formula is,

duu2+a2=ln|u+u2+a2|+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.

Where n is any real number

Calculation:

Consider the provided integral:

dx(3x+1)2+1

Multiply and divide the integral by 3,

133dx(3x+1)2+1

Let 3x+1=t

Now differentiate both the sides,

3dx=dt

The integral now becomes,

13dtt2+1

Now, use the formula duu2+a2

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