Problem 7
Partial Fractions with Repeated Linear Factors Evaluate \(\int \frac{x-2}{(2 x-1)^{2}(x-1)} d x .\)
Problem 7
Use the technique of completing the square to express each trinomial as the square of a binomial. $$ 2 x^{2}-8 x+3 $$
Problem 7
Find the integral by using the simplest method. Not all problems require integration by parts. $$ \left.\int \ln x d x \text { (Hint: } \int \ln x d x \text { is equivalent to } \int 1 \cdot \ln (x) d x .\right) $$
Problem 8
Find the integral by using the simplest method. Not all problems require integration by parts. $$ \int x \cos x d x $$
Problem 8
Integrating \(\int \cos ^{j} x \sin ^{k} x d x\) where \(k\) and \(j\) are Even Evaluate \(\int \sin ^{4} x d x\).
Problem 8
Use a table of integrals to evaluate the following integrals. $$ \int \frac{d y}{\sqrt{4-y^{2}}} $$
Problem 8
Use the technique of completing the square to express each trinomial as the square of a binomial. $$ -x^{2}-2 x+4 $$
Problem 8
Set up the partial fraction decomposition for \(\int \frac{x+2}{(x+3)^{3}(x-4)^{2}} d x .\) (Do not solve for the coefficients or complete the integration.)
Problem 8
Integrating a Discontinuous Integrand Evaluate \(\int_{-1}^{1} \frac{1}{x^{3}} d x\). State whether the improper integral converges or diverges.
Problem 9
Use a table of integrals to evaluate the following integrals. $$ \int \sin ^{3}(2 x) \cos (2 x) d x $$
