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Calc (trig ids, int, dX)

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valleystudent84's version from 2016-10-11 13:32

Section

 

Question Answer
Dx sinx = cosx
Dx cosx = -sinx
Dx Tanx = (secx)^2
Dx Cotx = -(cscx)^2
Dx secx = secxtanx
Dx cscx =-(cscxcotx)
Dx sinhx =coshx
Dx coshx =sinhx
Dx tanhx =1 - tanhx^2
Dx cothx =1 - cothx^2
Dx cschx =-cothxcschx
Dx sechx =-tanhxsechx
Dx arcsinu =dU/(a^2 - u^2)^1/2
Dx arctanu =dU/(a^2 + u^2)
Dx arcsecu =dU/[IuI(u^2 - a^2)^1/2]
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Question Answer
ᶴ (sinx) dX = -cosx + c
ᶴ (cosx) dX = sinx + c
ᶴ (tanx) =-ln IcosxI + c
ᶴ (cotx) =ln IsinxI + c
ᶴ (secxtanx) dX = secx + c
ᶴ (cscxcotx) dX = -cscx + c
ᶴ (secx) dX = ln Isecx+tanxI + c
ᶴ (cscx) dX = -ln Icscx+cotxI + c
ᶴ (secx)^2 dX = tanx + c
ᶴ (cscx)^2 dX = -cotx + c
ᶴ (sinhx) dX =coshx + c
ᶴ (coshx) dX =sinhx + c
ᶴ (tanhx) dX =ln IcoshxI + c
ᶴ (cschx) dX =ln Itanh(x/2)I + c
ᶴ (sechx) dX =acrtan(sinhx) + c
ᶴ (cothx) dX =ln IsinhxI + c
ᶴ (du)/(a^2 - u^2)^1/2 =arcsin(u/a) + c
ᶴ (du)/(a^2 + u^2) =(1/a)arctan(u/a) + c
ᶴ (du)/u(u^2 - a^2)^1/2 =(1/a)arcsec(IuI/a) + c
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Question Answer
ID* (sinx)^2 + (cosx)^2 = 1
ID* 1 + (tanx)^2 =(secx)^2
ID* 1 + (cotx)^2 =(cscx)^2
ID* tanx^2 Power reducing =(1 - cos2x)/(1 + cos2x)
ID* sin(2x) =2sinxcosx
ID* sinhx =(e^x - e^-x)/2
ID* coshx =(e^x + e^-x)/2
ID* tanhx =(e^x - e^-x)/(e^x + e^-x)
ID* (sinx)^2 Power reducing =(1-cos2x)/(2)
ID* (cosx)^2 Power reducing =(1+cos2x)/(2)
L I A T E for dU =(Logs) > (Inverse Trig) > (Algebraic ANY POWER) > (Trig REGULAR) > (Exponential)
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