Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on integration.
∫(2x-1) ln (3x) dx.

ln(3x)-x²/2 + x +c

Step-by-step explanation:

∫(2x-1) ln (3x) dx can be computed with parts. The ln part can be made simpler be derivating, and integrating a polynomial wont hurt us that much.

We can derivate ln(3x) using the chain rule, the derivate of ln(x) is 1/x and the derivate of 3x is 3; therefore

(ln(3x))' = (1/3x)*3 = 1/x

A primitive of (2x-1) is, on the other hand, x²-x

Hence

∫(2x-1) = ln(3x) (x²-x) - ∫(x²-x)/x dx = ln(3x) (x²-x) - ∫(x-1) dx = ln(3x) (x²-x) - (x²/2 - x + k) = ln(3x)-x²/2 + x +c

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.