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

Find the area under the curve of $y=\frac{10}{(x+2)(x+3)}$ between $x=0$ and $x=4$.

Express the integrand as a sum of partial fractions and evaluate the integral.

${\int }_{}^{}\frac{2}{x^3+x^2-x-1}dx$

Use the method of partial fractions to evaluate the integral.

${\int }_{}^{}\frac{5x^3-x^2+7x-2}{(x^2+1)(x^2+2)}dx$

Evaluate the integral.

${\int }_{}^{}\frac{t^4+t^2-2}{t^3+t}dt$

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))

7–84. Evaluate the following integrals.

45. ∫ from 0 to ln 2 [1 / (1 + eˣ)²] dx

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

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.

∫ (1 + tan x) sec²x dx