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Derivatives and Integral to Know

Terms in this set (31)

f'(cotx)
-csc²x
f'(cscx)
-cscx(cotx)
f'(aⁿ)
(lna)(aⁿ)
f'(sin⁻¹x)
1/√(1-x²)
f'(tan⁻¹x)
1/(1+x²)
f'(sec⁻¹x)
1/(|x|√(x²-1))
∫1dx
x + C
∫adx
ax + C
∫xⁿdx
(xⁿ⁺¹)/(n+1)+c, n≠-1
∫sinxdx
−cos(x)+C
∫cosxdx
sin(x) + C
∫sec²xdx
tanx+C
∫csc²xdx
-cot(x) + C
∫secxtanxdx
secx + C
∫cscxcotxdx
−cscx+C
∫(1/x)dx
ln|x| + C
∫eⁿdn
eⁿ+c
∫aⁿdn
aⁿ/ln(a) + C, a ≠1
∫1/√(1-x²)dx
sin⁻¹x + C
∫1/(1+x²)dx
tan⁻¹x + C
∫1/(|x|√(x²-1))dx
sec⁻¹x + C
∫sin(mx)dx =
(-1/m)cosmx + c
∫tan(mx)dx =
(-1/m)ln|cosmx| + c
∫cos(mx)dx =
(1/m)sinmx + c
∫cot(mx)dx =
(-1/m)ln|sinmx| + c
∫sec(mx)dx =
(1/m)ln|secmx + tanmx| + c
∫csc(mx)dx =
(1/m)ln|cscmx + cotmx| + c
∫dx/(a²+x²)
(1/a)tan⁻¹ (x/a) + c
∫dx/(x√x²-a²)
(1/a)sec⁻¹(|x|/a)+c
∫dx/√(a² - x²)
sin⁻¹(x/a)+C
∫udv = uv - ∫vdu; LIATE
integration by parts formula
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