Math — Fundamental Theorem & Techniques
FTC, integration by parts and by substitution.
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\int_a^b f(x)\,dx = F(b) - F(a)
\int u\,dv = uv - \int v\,du
\frac{d}{dx}\int_a^x f(t)\,dt = f(x)
\int_a^b f(g(x))g'(x)\,dx = \int_{g(a)}^{g(b)} f(u)\,du