Problem 2
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int x e^{3 x} d x $$
Problem 2
Perform the indicated integrations. $$ \int \sqrt{3 x} d x $$
Problem 2
In Problems \(1-16\), perform the indicated integrations. \(\int x \sqrt[3]{x+\pi} d x\)
Problem 2
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{2}{x^{2}+3 x} d x\)
Problem 2
Solve each differential equation. $$ (x+1) \frac{d y}{d x}+y=x^{2}-1 $$
Problem 3
Solve each differential equation. $$ \left(1-x^{2}\right) \frac{d y}{d x}+x y=a x,|x|<1 $$
Problem 3
\(\int \frac{t d t}{\sqrt{3 t+4}}\)
Problem 3
Perform the indicated integrations. $$ \int \sin ^{3} x d x $$
Problem 3
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int t e^{5 t+\pi} d t $$
Problem 3
Perform the indicated integrations. $$ \int_{0}^{2} x\left(x^{2}+1\right)^{5} d x $$
