Question

faca a integracacao g(t)=t^2/2-4/(t-3)+ 3t

Answer 1

$\displaystyle \text {g(t)}=\frac{\text t^2}{2}-\frac{4}{\text t-3}+3\text t \\\\\\ \int [\ \frac{\text t^2}{2}-\frac{4}{\text t-3}+3\text t\ ]\text{dt} \\\\\\ \int \frac{\text t^2}{2}\text{dt}-\int \frac{4}{\text t-3}\text{dt}+\int 3\text {t dt } \\\\\\ \frac{1}{2}\int \text t^2\text{dt} -4\int\frac{\text {dt}}{\text t-3}+3\int \text {t dt} \\\\\\ \frac{1}{2}.\frac{\text t^3}{3}-4.\text{ln}|\text t-3|+3.\frac{\text t^2}{2 } + \text C$

$\huge\boxed{\displaystyle \frac{\ \text t^3}{6}-4.\text{ln}|\text t-3| + \frac{3\text t^2}{2} + \text C\ }\checkmark$