Integration Using Log Rule Quiz

What is the integral of 1/(x-2) with respect to x?

• ln|x-2| + C

• ln|x| + C

• 1/(x-2) + C

• x ln|x-2| + C

In the second example, what substitution is made for dx?

• dx = 3 du

• dx = 2 du

• dx = du

• dx = 1/2 du

What is the integral of dx/(2x + 4) using the log rule?

• 2 ln|2x + 4| + C

• ln|2x + 4| + C

• 1/2 ln|2x + 4| + C

• 1/4 ln|2x + 4| + C

What is the simplified form of the integral of x/(3x^2 + 1) dx?

• 1/6 ln|3x^2 + 1| + C

• 1/6 ln|x^2 + 1| + C

• 1/3 ln|3x^2 + 1| + C

• ln|3x^2 + 1| + C

Why does the log rule not apply to the integral of dx/(x+4)^2?

• Because it results in a polynomial rule

• Because it results in a trigonometric rule

• Because it results in a logarithmic rule

• Because it results in a power rule

Which of the following integrals is not solved using the log rule?

• x/(3x^2 + 1) dx

• dx/(x+4)^2

• dx/(x ln x)

• dx/(x-2)

What substitution is used for the integral of dx/(x ln x)?

• u = x ln x

• u = ln x

• u = x

• u = 1/x

In the final example, what is the substitution for the integral of cos(x)/(2sin(x) - 1) dx?

• u = x

• u = cos(x)

• u = 2sin(x) - 1

• u = sin(x)

What is the derivative of ln(x)?

• x^2

• x

• 1/x

• ln(x)

What is the integral of dx/(x ln x) using the log rule?

• ln|ln x| + C

• ln|x ln x| + C

• ln|x| + C

• ln|1/x| + C