Indefinite integrals and substitution

The inverse of differentiation, plus substitution and integration by parts.

Definition

不定积分是求导的逆运算：F'(x) = f(x) 则 ∫f(x)dx = F(x) + C。换元法把复杂积分化为基本形式，分部积分对应乘积求导的逆。

Key formulas

• $\int f(x)\,dx = F(x) + C$

  定义

• $\int u\,dv = uv - \int v\,du$

  分部积分

Common mistakes

• 忘记 + C
• 换元后忘记换回原变量
• 分部积分选错 u 和 dv

Related topics

• Derivatives and rules