23-64. Integration Evaluate the following integrals.

44. ∫₁² 2/[t³(t + 1)] dt

23-64. Integration Evaluate the following integrals.

47. ∫ (x³ - 10x² + 27x)/(x² - 10x + 25) dx

23-64. Integration Evaluate the following integrals.

50. ∫ 8(x² + 4)/[x(x² + 8)] dx

23-64. Integration Evaluate the following integrals.

54. ∫ (z + 1)/[z(z² + 4)] dz

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

12. ∫ (8x + 5)/(2x² + 3x + 1) dx

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

63. ∫ dx/(x² - 2x - 15)

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

65. ∫ (from 0 to 1) dy/((y + 1)(y² + 1))

96. Challenge

Show that with the change of variables u = √tan x, the integral

∫ √tan x dx

can be converted to an integral amenable to partial fractions. Evaluate

∫[0 to π/4] √tan x dx.