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. $$ \int \sin ^{3} x d x $$
Problem 4
Perform the indicated integrations. $$ \int \cos ^{3} x d x $$
Problem 4
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int(t+7) e^{2 t+3} d t $$
Problem 4
In Problems 1-16, perform the indicated integrations. \(\int \frac{x^{2}+3 x}{\sqrt{x+4}} d x\)
Problem 4
Perform the indicated integrations. $$ \int_{0}^{1} x \sqrt{1-x^{2}} d x $$
Problem 4
A slope field is given for a differential equation of the form \(y^{\prime}=f(x, y) .\) Use the slope field to sketch the solution that satisfies the given initial condition. In each case, find \(\lim _{x \rightarrow \infty} y(x)\) and approximate \(y(2) .\) $$ y(1)=3 $$
Problem 4
Solve each differential equation. $$ y^{\prime}+y \tan x=\sec x $$
Problem 4
Evaluate the given integral. $$ \int \frac{x}{x^{2}-5 x+6} d x $$
Problem 4
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{5 x}{2 x^{3}+6 x^{2}} d x\)
