📋 Таблица интегралов

∫ xⁿ dx

= xⁿ⁺¹/(n+1) + C, n ≠ -1

∫ 1/x dx

= ln|x| + C

∫ eˣ dx

= eˣ + C

∫ aˣ dx

= aˣ/ln(a) + C

∫ sin(x) dx

= -cos(x) + C

∫ cos(x) dx

= sin(x) + C

∫ tan(x) dx

= -ln|cos(x)| + C

∫ cot(x) dx

= ln|sin(x)| + C

∫ 1/cos²(x) dx

= tan(x) + C

∫ 1/sin²(x) dx

= -cot(x) + C

∫ 1/(1+x²) dx

= arctan(x) + C

∫ 1/√(1-x²) dx

= arcsin(x) + C

∫ 1/(x²+a²) dx

= (1/a)·arctan(x/a) + C

∫ 1/√(x²+a²) dx

= ln|x + √(x²+a²)| + C

∫ 1/√(a²-x²) dx

= arcsin(x/a) + C

∫ sinh(x) dx

= cosh(x) + C

∫ cosh(x) dx

= sinh(x) + C

∫ ln(x) dx

= x·ln(x) - x + C

∫ 1/(x²-a²) dx

= (1/2a)·ln|(x-a)/(x+a)| + C

∫ √(a²-x²) dx

= (x/2)·√(a²-x²) + (a²/2)·arcsin(x/a) + C