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Level 574

Integrals


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∫x^n dx
(x^n+1)/(n+1) + c
∫cosx dx
sinx + c
∫sinx dx
-cosx + c
∫-sinx dx
cosx + c
∫-cosx dx
-sinx + c
∫sec^2x dx
tanx + c
∫secx tanx dx
secx + c
∫csc^2x dx
-cotx + c
∫cscx cotx dx
-cscx + c
∫e^x dx
e^x + C
∫1/x dx
ln|x| + c
∫secx dx
ln|secx + tanx| + c
∫tanx dx
ln|secx| + c
∫cotx dx
ln|sinx| + c
∫cscx dx
-ln|cscx + cotx| + c
arcsin(x/a) + c
∫1/(sqrt(a^2 - x^2)) dx
∫1/(x^2 + a^2) dx
1/a * arctan(x/a) + c
1/a * arcsec(x/a) + c
∫1/(sqrt(x^2 - a^2) * |x|) dx
f'(sinx)
cosx
f'(cosx)
-sinx
f'(tanx)
sec^2x
f'(cotx)
-csc^2x
f'(secx)
secx*tanx
f'(cscx)
-cscx*cotx
f'(arcsinx)
1/√(1-x^2)
f'(arccosx)
-1/√(1-x^2)
f'(arctan)=
1/(x^2+1)
f'(arccot)
-1/(x^2+1)
f'(arcsec)
1/(sqrt(x^2-1))|x|
f'(arccsc)
-1/(sqrt(x^2-1))|x|
1
sin^2(Θ) + cos^2(Θ)
cot^2(Θ)
csc^2(Θ) - 1
tan^2(Θ)
sec^2(Θ) - 1
If integrand involves sqrt(a^2 - x^2)
x = asinθ → radical = acosθ
If integrand involves sqrt(a^2 + x^2)
x = atanθ → radical = asecθ
If integrand involves sqrt(x^2 - a^2)
x = asecθ → radical = atanθ
sin^2(Θ)
(1 - cos(2Θ)) / 2
cos^2(Θ)
(1 + cos(2Θ)) / 2
tan^2(Θ) (double angle)
(1 - cos(2Θ))/(1 + cos(2Θ))
Integral sinx dx
-cosx + C
Integral tanx dx
Ln (abs secx) + C
Integral secx dx
Ln (abs secx+tanx) + C
Integral cosx dx
Sinx + c
Integral cotx dx
Ln (abs sinx) + C
Integral cscx dx
Ln (abs cscx-cotx) + C
Integral 1/x dx
Ln (abs x) + C
Integral e^x dx
E^x + C
Integral x^n dx
(1/n+1)x^(n+1) + C
Integral b^x dx
b^x/lnb + C