Problem 4
Evaluating an Improper Integral on \((-\infty,+\infty)\) Evaluate \(\int_{-\infty}^{+\infty} x e^{x} d x\). State whether the improper integral converges or diverges.
Problem 4
Dividing before Applying Partial Fractions Evaluate \(\int \frac{x^{2}+3 x+1}{x^{2}-4} d x\)
Problem 4
Use the midpoint rule with \(n=2\) to estimate \(\int_{1}^{2} \frac{1}{x} d x\).
Problem 4
Use a table of integrals to evaluate the following integrals. $$ \int \frac{1}{\sqrt{x^{2}+6 x}} d x $$
Problem 5
In using the technique of integration by parts, you must carefully choose which expression is u. For each of the following problems, use the guidelines in this section to choose u. Do not evaluate the integrals. $$ \int e^{3 x} \sin (2 x) d x $$
Problem 5
Simplify the following expressions by writing each one using a single trigonometric function. $$ 16 \cosh ^{2} \theta-16 $$
Problem 5
Applying Partial Fractions after a Substitution Evaluate \(\int \frac{\cos x}{\sin ^{2} x-\sin x} d x\).
Problem 5
Evaluate \(\int_{-3}^{+\infty} e^{-x} d x\). State whether the improper integral converges or diverges.
Problem 5
Integrating an Even Power of \(\sin x\) Evaluate \(\int \sin ^{2} x d x\).
Problem 5
Use a table of integrals to evaluate the following integrals. $$ \int \frac{x}{x+1} d x $$
