Use integration by parts to derive the following formula from the table of integrals.
∫x^n . ln |x|dx=x^n+1 [ln |x|/n+1]-1/(n+1)^2]+c, n≠-1.

Step-by-step explanation:

We have been given an indefinite integral . We are asked to integrate it.

We will use integration by pats to solve our given problem.

Let and .

Now, we need to find du and v using above values.

Substitute these values in integration by parts formula:

Therefore, our required integral would be .

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.