Problem 7
In Problems 1-16, perform the indicated integrations. \(\int t(3 t+2)^{3 / 2} d t\)
Problem 8
Evaluate the given integral. $$ \int_{0}^{1 / 2} \frac{1}{1-t^{2}} d t $$
Problem 8
In Problems 1-16, perform the indicated integrations. \(\int x(1-x)^{2 / 3} d x\)
Problem 8
Perform the indicated integrations. $$ \int\left(\sin ^{3} 2 t\right) \sqrt{\cos 2 t} d t $$
Problem 8
Solve each differential equation. $$ y^{\prime}+\frac{2 y}{x+1}=(x+1)^{3} $$
Problem 8
Plot a slope field for each differential equation. Use the method of separation of variables (Section 4.9) or an integrating factor (Section 7.7) to find a particular solution of the differential equation that satisfies the given initial condition, and plot the particular solution. $$ y^{\prime}=-y ; y(0)=4 $$
Problem 8
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{x+\pi}{x^{2}-3 \pi x+2 \pi^{2}} d x\)
Problem 8
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int(x-\pi) \sin x d x $$
Problem 8
Perform the indicated integrations. $$ \int \frac{2 t^{2}}{2 t^{2}+1} d t $$
Problem 9
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{2 x+21}{2 x^{2}+9 x-5} d x\)
