Chapter 13.5, Problem 6CP

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# True or false: ∫ x 2 + 4 d x can be evaluated with formula 1, formula 6, or formula 16.

To determine

Whether the given integral x2+4 dx can be evaluated using the formula undu=un+1n+1+C or u2+a2 du=12(uu2+a2+a2ln|u+u2+a2|)+C or uau+b du=2(3au2b)(au+b)3215a2+C.

Explanation

Given Information:

The provided integral is x2+4 dx.

Explanation:

Consider the provided integral: x2+4 dx

The given integral is not in the form of first formula. So, the integral can't be evaluated using the first formula.

Now, again consider the given integral: x2+4 dx

The given integral is in the form of second formula. So, it can be evaluated using the second formula.

x2+4 dx= x2+22 dx

The second formula that is u2+a2 du=12(uu2+a2+a2ln|u+u2+a2|)+C can be used to evaluate the given integral.

x2+22 dx=12(xx2+4+4ln|x+x2+4|)+C.

Again consider the given integral: x2+4 dx

The given integral is not in the form of third formula

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