Problem 2
Evaluate \(\int \frac{x-3}{x+2} d x\)
Problem 2
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. $$ \int x^{3} \ln (x) d x $$
Problem 3
Partial Fractions with Nonrepeated Linear Factors Evaluate \(\int \frac{3 x+2}{x^{3}-x^{2}-2 x} d x\)
Problem 3
Use a table of integrals to evaluate the following integrals. $$ \int x^{3} \sqrt{1+2 x^{2}} d x $$
Problem 3
Evaluating an Improper Integral over an Infinite Interval Evaluate \(\int_{-\infty}^{0} \frac{1}{x^{2}+4} d x\). State whether the improper integral converges or diverges.
Problem 3
A Preliminary Example: Integrating \(\int \cos j x \sin ^{k} x d x\) Where \(k\) is Odd Evaluate \(\int \cos ^{2} x \sin ^{3} x d x\).
Problem 3
Simplify the following expressions by writing each one using a single trigonometric function. $$ a^{2}+a^{2} \tan ^{2} \theta $$
Problem 4
Evaluate \(\int \cos ^{3} x \sin ^{2} x d x\)
Problem 4
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. $$ \int x^{2} \arctan x d x $$
Problem 4
Use the midpoint rule with \(n=2\) to estimate \(\int_{1}^{2} \frac{1}{x} d x\).
