∫ u dv = uv -∫v du (Integration by parts)

∫ xⁿ dx = xⁿ⁺¹ / n+1 + c

∫ e^x dx = e^x + c

∫ 1/x dx = log x + c

∫ 1/ x² dx = - 1/x + c

∫ Sin x dx = - Cos x + c

∫ Cos x dx = Sin x + c

∫ Sin ax dx = - Cos ax /a + c

∫ Cos ax dx = Sin ax /a + c

∫ Tan x Sec x dx = Sec x + c

∫ Sec² x dx = Tan x + c

∫ Cosec² x dx = - Cot x + c

∫ Cot x Cosec x dx = - Cosec x + c

∫ √x dx = x^3/2 / 3/2 + c

∫ 1/√x dx = 2√x + c

∫ Tan x dx = log Sec x + c

∫ Sec x dx = log (Sec x + Tan x) + c

∫ Cosec x dx = - log (Cosec x + Cot x) + c

∫ x dy + y dx = xy + c

∫ Cot x dx = = log Sin x + c

∫ dx/√ (a² - x²) = Sin^-1 x/a + c

∫ dx/√ (a² + x²) = log(x + √ (a² + x²)) + c

∫ dx/√(x² - a²) = Cos^-1 x/a + c or log(x + √(x² - a²)) + c

∫ dx/( a² + x²) = 1/a Tan^-1 x/a + c

∫ dx/( a² - x²) = 1/2a log((a+x)/(a-x)) + c

∫ dx/(x² - a²) = 1/2a log((x-a)/(x+a)) + c

∫ √ (a² - x²) dx = x/a √ (a² - x²) + a²/2 Sin^-1 x/a + c

∫ √ (a² + x²) dx = x/2 √ (a² + x²) + a²/2 log(x + √ (a² + x²)) + c

∫ √(x² - a²) dx = x/2 √(x² - a²) - a²/2 log(x + √(x² - a²)) + c