Problem 1
Solve each differential equation. $$ \frac{d y}{d x}+y=e^{-x} $$
Problem 1
In Problems 1-54, perform the indicated integrations. $$ \int(x-2)^{5} d x $$
Problem 1
Perform the indicated integrations. $$ \int \sin ^{2} x d x $$
Problem 1
$$ \text { In Problems 1-36, use integration by parts to evaluate each integral. } $$ $$ \int x e^{x} d x $$
Problem 1
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{1}{x(x+1)} d x\)
Problem 1
In Problems \(1-16\), perform the indicated integrations. \(\int x \sqrt{x+1} d x\)
Problem 1
In Problems 1-12, evaluate the given integral. $$ \int x e^{-5 x} d x $$
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
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int x e^{3 x} d x $$
Problem 2
Perform the indicated integrations. $$ \int \sin ^{4} 6 x d x $$
