Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.
Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.
Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.
Give the partial fraction decomposition for the following expression using strategic substitutions for .
Express the rational function as a sum or difference or simpler rational expressions.
Express the rational function as a sum or difference or simpler rational expressions.
Evaluate the integral.
Evaluate the integral.
Evaluate the integral.
Find the area under the curve of between and .
Express the integrand as a sum of partial fractions and evaluate the integral.
Use the method of partial fractions to evaluate the integral.
Evaluate the integral.
7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
21. ∫ cos x / (sin² x + 2 sin x) dx
7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
34. ∫ dx / (x(x¹⁰ + 1))
Choosing an integration strategy Identify a technique of integration for evaluating the following integrals. If necessary, explain how to first simplify the integrand before applying the suggested technique of integration. You do not need to evaluate the integrals.
∫ (5x² + 18x + 20) / [(2x + 3)(x² + 4x + 8)] dx