Calculus

• The limit of a function is the value that the function approaches as the input approaches a certain value.
• • ∫ 1 dx = x + C
• • ∫ a dx = ax+ C
• • ∫ xn dx = ((xn+1)/(n+1))+C ; n≠1
•  sin x dx = – cos x + C
• • ∫ cos x dx = sin x + C
• • ∫ sec2x dx = tan x + C
• • ∫ csc2x dx = -cot x + C
• • ∫ sec x (tan x) dx = sec x + C
• • ∫ csc x ( cot x) dx = – csc x + C
• • ∫ (1/x) dx = ln |x| + C
• • ∫ ex dx = ex+ C
• • ∫ ax dx = (ax/ln a) + C ; a>0,  a≠1
• • ∫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 = 1/2a log|(x - a)(x + a| + C
• • ∫ 1/(a2 - x2) dx =1/2a log|(a + x)(a - x)| + C
• • ∫1/(x2 + a2) dx = 1/a tan-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