Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 27

$$\frac{1}{40}( 4x+5)^{10}$$

Given $$ \int(4 x+5)^{9} d x$$ Let $$ u= 4x+9\ \ \ \Rightarrow\ \ du=4dx$$ Then \begin{align*} \int(4 x+5)^{9} d x&=\frac{1}{4}\int u^{9} d u\\ &=\frac{1}{40}u^{10}\\ &= \frac{1}{40}( 4x+5)^{10} \end{align*}