91Ó°ÊÓ

Find each integral by using the integral table on the inside back cover. $$ \int \frac{1}{x^{2}-25} d x $$

Integration by parts often involves finding integrals like the following when integrating \(d v\) to find \(v\). Find the following integrals without using integration by parts (using formulas 1 through 7 on the inside back cover). Be ready to find similar integrals during the integration by parts procedure. $$ \int(x-5)^{6} d x $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=x y-1 $$

Evaluate each limit (or state that it does not exist). $$ \lim _{x \rightarrow-\infty} \frac{1}{x^{3}} $$

Find each integral by using the integral table on the inside back cover. $$ \int \frac{1}{x^{2}(2 x+1)} d x $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=6 x^{2} y $$

$$ \text { Use integration by parts to find each integral. } $$ $$ \int x e^{2 x} d x $$

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. (Do not solve, just identify the type.) \(y^{\prime}=y(6-y)\)

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=12 x^{3} y $$

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. (Do not solve, just identify the type.) \(y^{\prime}=0.01\left(100-y^{2}\right)\)