Indefinite Integral

∫ a dx = ax + c

where a and c are constants

where a and c are constants, n is an integer and n ≠ –1

Addition or subtraction rule

∫ [f (x) ± g(x)] dx = ∫ f (x) dx ± ∫ g(x) dx

Given the gradient function dy/dx = f'(x),

the equation of curve for that function is y = ∫ f'(x) dx

where a and b are constants, n is an integer and n ≠ –1

Integration

reverse process of differentiation

If d/dx[ f (x)] = f'(x),

then the integral of f'(x) with respect to x is ∫ f'(x) dx = f (x)

Indefinite integrals

Substitution method

Indefinite integral for functions in the form of (ax+b)^n, where a and b are constants, n is an integer and n ≠ –1

The equation of the curve

can be obtained from the gradient function by integration