Integration

Integration Formula

∫ xn dx = x(n + 1)/(n + 1)+ C
∫ 1 dx = x + C
∫ ex dx = ex + C
∫ 1/x dx = log |x| + C
∫ ax dx = ax /log a+ C
∫ ex [f(x) + f'(x)] dx = ex f(x) + C
∫ cos x dx = sin x + C
∫ sin x dx = -cos x + C
∫ sec2x dx = tan x + C

^{∫ cosec2x dx = -cot x + C
∫ sec x tan x dx = sec x + C
∫ cosec x cot x dx = -cosec x + C
∫ tan x dx = log |sec x| + C
∫ cot x dx = log |sin x| + C
∫ sec x dx = log |sec x + tan x| + C
∫ cosec x dx = log |cosec x - cot x| + C
∫ 1/√(1 - x²)dx = sin^-1x + C
∫ 1/√(1 - x²)dx = -cos^-1x + C
∫ 1/(1 + x²)dx = tan^-1x + C
∫ 1/(1 + x² )dx = -cot^-1x + C
∫ 1/x√(x² - 1)dx = sec^-1x + C
∫ 1/x√(x² - 1)dx = -cosec^-1 x + C
∫ 1/(x² - a²)dx = 1/2 alog|(x - a)(x + a| + C
∫ 1/(a² - x²)dx =1/2 alog|(a + x)(a - x)| + C
∫ 1/(x² + a²)dx = 1/ atan^-1x/a + C
∫ 1/√(x² - a²)dx = log |x +√(x² - a²)| + C
∫ √(x² - a²)dx = x/2 √(x² - a²) -a²/2 log |x + √(x² - a²)| + C
∫ 1/√(a² - x²)dx = sin^-1 x/a + C
∫ √(a² - x²)dx = x/2 √(a² - x²) dx + a²/2 sin^-1 x/a + C
∫ 1/√(x² + a² )dx = log |x + √(x² + a²)| + C
∫ √(x² + a² )dx = x/2 √(x² + a² )+ a²/2 log |x + √(x² + a²)| + C
∫ 1/(x²+a²)dx=1/(atan^–1xa+c}