Indefinite Integration

Basic integration rules

Basic integration rules: ∫x^n dx = x^(n+1)/(n+1) + c (n≠-1), ∫1/x dx = log|x| + c, ∫e^x dx = e^x + c, ∫a^x dx = a^x/log a + c, ∫sin x dx = -cos x + c,

Used when integrand is of

Used when integrand is of the form f(g(x))·g'(x). Put g(x) = t, then g'(x)dx = dt. Example: ∫3x²sin(x³)dx, let x³ = t, then 3x²dx = dt, so integral be

For products of functions

For products of functions: ∫u·v dx = u∫v dx - ∫(du/dx)(∫v dx)dx. Use LIATE order for choosing u: Logarithmic, Inverse trigonometric, Algebraic, Trigon

Decomposes rational functions f(x)/g(x) into simpler

Decomposes rational functions f(x)/g(x) into simpler fractions. For (px²+qx+r)/((x-a)(x-b)(x-c)) = A/(x-a) + B/(x-b) + C/(x-c). Find A, B, C by substi

Seven important forms

Seven important forms: ∫1/(x²+a²)dx = (1/a)tan⁻¹(x/a) + c, ∫1/(x²-a²)dx = 1/(2a)log|(x-a)/(x+a)| + c, ∫1/√(a²-x²)dx = sin⁻¹(x/a) + c, ∫1/√(x²±a²)dx =