Integration techniques and improper integrals

By the end you’ll be able to

• Evaluate integrals by substitution, integration by parts (including tabular and cyclic cases), partial fractions and trigonometric substitution
• Integrate powers and products of trigonometric functions, and simplify definite integrals using odd/even symmetry and the substitution $x \mapsto a + b - x$
• Evaluate improper integrals over infinite intervals or with unbounded integrands, and decide convergence by comparison with $\int_1^\infty x^{-p}\,dx$ and $\int_0^1 x^{-p}\,dx$