Math Problem Statement

Consider the following. 9

x ln(x) dx

The integrand 9

x ln(x) can be rewritten as the product of which two functions?

(ln(x))−1 and 9x1/2

(ln(x))−1 and 9x−1/2

ln(x) and 9x1/2

ln(x) and 9x−1/2 Correct: Your answer is correct. Outstanding! Which of the two functions is most easily integrated?

Correct: Your answer is correct. That's right! Use integration by parts to evaluate the integral. (Remember the constant of integration.)

Incorrect: Your answer is incorrect.

Check your answer by taking the derivative.

Solution

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Math Problem Analysis

Mathematical Concepts

Integration
Logarithmic Functions
Product of Functions
Integration by Parts

Formulas

Integration by parts: ∫u dv = uv - ∫v du
Logarithmic differentiation: d(ln(x))/dx = 1/x
Polynomial integration: ∫x^n dx = (x^(n+1))/(n+1) + C

Theorems

Integration by Parts Theorem

Suitable Grade Level

Undergraduate Calculus