Use the power rule: (int x^n,dx=frac{x^{n+1}}{n+1}+C), (nneq -1)
Use the constant rule: (int c,dx=cx+C)
Use the constant multiple rule: (int c,f(x),dx=cint f(x),dx)
Use the sum/difference rule: (int [f(x)pm g(x)],dx=int f(x),dxpmint g(x),dx)
Use substitution: let (u=g(x)), replace (dx) accordingly, integrate in (u), then substitute back
Use integration by parts: (int u,dv=uv-int v,du)
Use trigonometric identities to simplify before integrating
Use partial fractions for rational functions
Use trigonometric substitution for radicals like (sqrt{a^2-x^2}), (sqrt{a^2+x^2}), (sqrt{x^2-a^2})
Use standard integral formulas for common functions
Use symmetry for definite integrals when applicable
Use numerical methods when an antiderivative is not elementary
Add the constant of integration (C) for indefinite integrals