# Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 48

$$f(x)= \frac{1}{3}(x+1)^3+ \frac{25}{3}$$

#### Work Step by Step

Given: Slope$=(x+1)^2$ and passes through $(-2,8)$ Since the curve is given by \begin{align*} f(x)&=\int (x+1)^2dx\\ &=\frac{1}{3}(x+1)^3+c \end{align*} Since the curve passes through $(-2,8)$, then $c=25/3$ and $$f(x)= \frac{1}{3}(x+1)^3+ \frac{25}{3}$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.