71. \int_0^1 x^p \ln x \, dx
33. \int_0^\infty e^{-\sqrt{y}} \, dy
12. \int_0^\infty \frac{1}{\sqrt{1 + x}} \, dx
57. \int_0^\infty \frac{x}{x^3 + 1} \, dx
58. \int_1^\infty \frac{1 + \sin^2 x}{\sqrt{x}} \, dx
59. \int_2^\infty \frac{x - \ln x}{x} \, dx
60. \int_0^1 \frac{\arctan x}{2 + e^x} \, dx
61. \int_1^\infty \frac{x^4 + 1}{\sqrt{x^4 - x}} \, dx
62. \int_1^\infty \frac{2 + \cos x}{\sqrt{x^4 + x^2}} \, dx
