Integral formulas Flashcards
be able to define integral fomulas
∫f(x) dx = ??
f(x)’ + c
∫dx = ??
∫dy = ??
x + c
y + c
∫a dx = ?? (a = constant)
a ∫dx
= ax + c
∫ [ f₁ (x) ± f₂ (x) ] dx = ??
∫ [ f₁ (x) ]dx ± ∫ [f₂ (x) ]dx + c
[you can seperate the two functions into two integral equations]
general power formula
∫ uⁿ du = ??
u^n+1 / n+1 + c
[n cannot equal -1]
what do you have to add at the end of every integration?
+c [constant]
Integration of Log functions formula
∫ du/ u = ??
ln | u| = c
Integration of exponential functions formula
∫ eᵘ du = ??
eᵘ + c
Integration of exponential functions formula
∫ aᵘ du = ??
aᵘ/ ln a + c
∫sin u du
-cos u + c
∫cos u du
sin u + c
∫sec^2 u du
tan u + c
∫csc^2 u du
-cot u + c
∫sec u tan u du
sec u + c
∫csc u cot u du
-csc u + c
∫tan u du
ln sec u + c
∫cot u du
ln sin u + c
∫sec u du
ln (sec u + tan u) + c
∫csc u du
-ln (csc u + cot u) + c
∫du/√a² - u²
arc sin u/a + c
∫du/ a² + u²
1/a arc tan u/a + c
∫du/u√u² - a²
1/a arc sec u/a + c
∫udv
uv - ∫vdu + c
