Solving a directly-integrable equation is easy: First solve for the derivative to get the equation into form (2.1) or (2.1′), then integrate both sides as many times as needed to eliminate the derivatives, and, finally, do whatever simplification seems appropriate. dx − 4x = 6 .

The list of basic integral formulas is given below: ∫ 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.

Differentiation reveals the rate-of-change (or instantaneous rate-of-use) of the original quantity or equation. Integration reveals the cumulative effect of the original quantity or equation.

Basically, integration is a way of uniting the part to find a whole. It is the inverse operation of differentiation. Thus the basic integration formula is ∫ f'(x) dx = f(x) + C. Using this, the following integration formulas are derived.

We can solve these differential equations using the technique of an integrating factor. We multiply both sides of the differential equation by the integrating factor I which is defined as I = e∫ P dx.

Integration formulas are the formulas which are used to solve various integration problems, ∫ 1 dx = x + C. ∫ xn dx = x(n + 1)/(n + 1)+ C. ∫ 1/x dx = log |x| + C.