Evaluate the Integral $\int 15 x \ln (1+x) d x$ A) $15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x)+\frac{1}{3} \ln (1+x)\right)+C$

question 9

Multiple Choice

Evaluate the integral. $\int 15 x \ln (1+x) d x$

• A) \(15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x)+\frac{1}{3} \ln (1+x)\right)+C\)
• B) \(\frac{15}{4}\left(2\left(x^{2}-1\right) \ln (1+x)-x(x-2)\right)+C\)
• C) \(15\left(\frac{1}{4} x^{2}-\frac{1}{2} \ln (1+x)+\frac{x^{2}}{2}(\ln (1+x))\right)+C\)
• D) \(\frac{15}{4}\left(2\left(x^{2}-1\right) \ln (1+x)+x(x-2)\right)+C\)
• E) \(15\left(-\frac{1}{3} x+\frac{1}{6} x^{2}-\frac{1}{9} x^{4}+\frac{1}{3} \ln (1+x)\right)+C\)

---

Definitions:

Visual Representation

The use of images, diagrams, or animations to convey information or ideas to an audience.

Consumer Touchpoints

Points of interaction between a consumer and a product, brand, or company throughout the buying and usage process.

Purchase Decision Process

The sequence of steps consumers go through, from recognizing a need, evaluating alternatives, to making the purchase decision and post-purchase evaluation.

Consumption Strategy Model

A framework for understanding how consumers plan and select among products and services to satisfy their needs.