Antiderivative Rules

Question 1

Power Rule

Answer 1

∫x^n = (x^n+1/n) + c
Example:
x^4 -> (x^5/5) + c

Question 2

Constant Rule

Answer 2

∫C = Cx + c
∫4 = 4x + c

Question 3

Sum Rule

Answer 3

∫f(x) + g(x) = ∫f(x) + ∫g(x)

Question 4

Exponential Rule

Answer 4

∫e^x = e^x + c

Question 5

ln / Quotient Rule

Answer 5

∫1/x = ln|x| + c

Question 6

Integration by parts

Answer 6

∫udv = uv - ∫vdu
Can be rewrote as:
∫f(x)g(x)dx = f(x)F(g(x)) - ∫(F(g(x))) f’(x)
With F(x) representing the antiderivative of x.