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 .

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step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!