Other Properties of Integrals

Additional useful facts beyond linearity and inverse differentiation.

Shift by constant: $\int f(x+a)\,dx = \int f(u)\,du$ with $u=x+a$ (captures translation).
Symmetry hints (for indefinite forms, prepare for definite use).
Composition caution: no general rule for $\int f(g(x))dx$ without substitution; choose proper methods.
Integrability: continuity implies integrability; piecewise/with finite discontinuities often integrable (for definite case context).

Summary

符号	类型	读音/说明	在本文中的含义
$\int$	数学符号	integral	不定积分符号