Olá, Érica.
[tex] \int \frac1{x^2} + \frac2{x^3} + 3\sqrt x\ dx=\int x^{-2}+2x^{-3}+3x^{\frac12}\ dx=\\\\ \text{Como }\int x^n = \frac{x^{n+1}}{n+1},\text{ temos}:\\\\ =\frac{x^{-2+1}}{-2+1}+2 \cdot \frac{x^{-3+1}}{-3+1}+3\cdot \frac{x^{\frac12+1}}{\frac12+1}=\\\\ =\frac{x^{-1}}{-1}+2 \cdot \frac{x^{-2}}{-2}+3\cdot\frac{x^{\frac32}}{\frac32}=\\\\ =-\frac1{x}-\frac1{x^2}+3\cdot\frac23\sqrt{x^3}=\\\\ =-\frac1{x}-\frac1{x^2}+2\sqrt{x^3}[/tex]
