Problem 1
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. $$ \int x^{3} e^{2 x} d x $$
Problem 1
Finding an Area Determine whether the area between the graph of \(f(x)=\frac{1}{x}\) and the \(x\) -axis over the interval \([1,+\infty)\) is finite or infinite.
Problem 1
Use a table of integrals to evaluate the following integrals. $$ \int_{0}^{4} \frac{x}{\sqrt{1+2 x}} d x $$
Problem 1
Integrating \(\int \frac{P(x)}{Q(x)} d x\), where \(\operatorname{deg}(P(x)) \geq \operatorname{deg}(Q(x))\) Evaluate \(\int \frac{x^{2}+3 x+5}{x+1} d x\).
Problem 1
Simplify the following expressions by writing each one using a single trigonometric function. $$ 4-4 \sin ^{2} \theta $$
Problem 1
Integrating \(\int \cos ^{\prime} x \sin x d x\) Evaluate \(\int \cos ^{3} x \sin x d x\)
Problem 2
Evaluate \(\int \sin ^{4} x \cos x d x\)
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 2
Use a table of integrals to evaluate the following integrals. $$ \int \frac{x+3}{x^{2}+2 x+2} d x $$
Problem 2
Evaluate \(\int \frac{x-3}{x+2} d x\)
