Chandler Conner

07/27/2024 · escuela secundaria

9(a) Find \( \int \frac{x+2}{x^{2}+2 x-3} \mathrm{~d} x \) \( \begin{array}{ll}\text { (b) Find } \int 2 x \sin x \mathrm{~d} x\end{array} \) \( \begin{array}{ll}\text { (c) Using the substitution } x=3 \sin \theta \text {, find the exact value of } \int_{0}^{\frac{3}{2}} \sqrt{9-x^{2}} \mathrm{~d} x \\ 9 & \text { (a) } \frac{3}{4} \ln |x-1|+\frac{1}{4} \ln |x+3|+C \text { or } \frac{1}{2} \ln \left|x^{2}+2 x-3\right|+\frac{1}{4} \ln \left|\frac{x-1}{x+3}\right|+C \\ \text { (b) }-2 x \cos x+2 \sin x+C & \text { (c) } \frac{9}{8} \sqrt{3}+\frac{3}{4} \pi\end{array} \) \( \begin{array}{ll}\text { (b) }\end{array} \)