Integration Flashcards
d/dx integral f(x) dx
f(x)
Integral dF(x)
F(x) + c
Integral cf(x) dx
c integral f(x) dx
integral (f(x) +/- g(x)) dx
Integral f(x) dx +/- integral g(x) dx
Integral between a and b f(x) dx
- integral between b and a f(x) dx
Integral between a and a f(x) dx
0
Integral between a and b cf(x) dx
c integral between a and b f(x) dx
Integral between a and c f(x) dx + integral between c and b f(x) dx
Integral between a and b f(x) dx
Integral dx
x + C
Integral x^(n) dx
(x^(n+1))/(n+1) + C
Integral dx/x
ln |x| + C
Integral dx/(1 + x^2)
arctanx + C
Integral dx/(1-x^2)^1/2
arcsinx + c
Integral e^x dx
e^x + C
Integral a^x dx
a^x/ln(a) + C
Integral sinx dx
- cosx + C
Integral cosx dx
sinx + C
Integral dx/(cos^(2)x)
tanx + C
Integral dx/(sin^(2)x)
- cotx + C
Integral sinhx dx
coshx + C
Integral coshx
sinhx + c
Integral dx/(cosh^(2)x)
tanhx + C
Integral dx/(sinh^(2)x)
cothx + C
Integral dx/(1 - x^(2))
1/2 ln|(1+x)/(1-x)| + C
Integral dx/(x^(2) +/- 1)^1/2
ln |x + (x^(2) +/- 1)| + C
Possible substitutions for (a^(2) - x^(2))^1/2
x = asinu or x = atanhu
Possible substitutions for (a^(2) + x^(2))^1/2
x = asinhu or x = atanu
Possible substitutions for (x^(2) - a^(2))^1/2
x = acoshu or x = a/cosu
Possible substitutions for trigonometric functions
u = tan(x/2) or u = sinx or u = cosx
Possible substitutions for hyperbolic functions
u = e^x or u = sinhx or u = coshx or u = tanh(x/2)
