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Level 620

Common Integrals, Derivatives & Trigonometric Iden


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∫f'(x)/f(x) dx =
ln |f(x)| + C
-csc²x
f'(x) of cot x
-cscxcotx
d/dx (csc x) =
∫cosx dx =
sinx + C
-cosx + c
∫sinx dx =
tanx + c
∫sec²x dx =
-cotx +C
∫csc²x dx =
secx + C
∫secxtanx dx =
-cscx + C
∫ cscx cotx dx
∫tanx dx =
ln | secx | +C
∫cotx dx =
ln | sinx | +C
∫secx dx =
ln | secx + tanx | +C
∫cscx dx =
ln | cscx - cotx | +C
∫xⁿ dx =
[xⁿ⁺¹ / (n + 1)] +C; n ≠ -1
∫(1/x) dx =
ln | x | +C
∫eⁿ dx
eⁿ +C
k∫f(x) dx
∫k f(x) dx (where k is a constant) =
∫f(x) dx ± ∫g(x) dx
∫ [f(x) ± g(x)] dx =
Integration by parts equation
∫u(dv/dx) dx = uv - ∫v(du/dx) dx
cscx
1/sinx
secx
1/cosx
cotx
1/tanx
1
sin²x + cos²x
csc²x
1+cos²x (Pythagorean Identities)
2sinxcosx
sin 2x
cos2x
cos²x - sin²x
sin(-x)
-sinx
cos(-x)
cosx
tan(-x)
-tanx
csc(-x)
-csc(x)
sec(-x)
sec(x)
cot(-x)
-cot(x)
sinAcosB+cosAsinB
sin(A + B)
sinAcosB-cosAsinB
sin(A - B)
cosAcosB-sinAsinB
cos(A + B)
cosAcosB + sinAsinB
cos(A - B)