Which of the following integrals cannot be evaluated using a simple substitution? (4 points) select one:

a. the integral of the square root of the quantity x minus 1, dx
b. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
c. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
d. the integral of x times the square root of the quantity x squared minus 1, dx

B. and C.

General Formulas and Concepts:

Calculus

Differentiation

Integration

U-Substitution

Step-by-step explanation:

*Note:

It seems like B and C are both the same answer.

Let's define our answer choices:

a.  

b.  

c.  

d.  

Let's run u-substitution through each of the answer choices:

a.  

∴ answer choice A can be evaluated with a simple substitution.

b.  

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice B cannot be evaluated using a simple substitution.

C.  

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice C cannot be evaluated using a simple substitution.

D.  

Using a little rewriting and integration properties, this integral can be evaluated using a simple substitution.

∴ answer choice D can be evaluated using a simple substitution.

Out of all the choices, we see that B and C cannot be evaluated using a simple substitution.

∴ our answer choices should be B and C.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e