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31 Cards in this Set

  • Front
  • Back

ad: x^n

x^n+1/n+1+c

ad: sinx

-cosx+c

ad: cosx

sinx+c

ad: sec^2x

tanx+c

ad: csc^2

-cot x+c

ad: secxtanx

secx+c

ad: e^x

e^x+c

ad: a^x

a^x/ln a +C

1/(1-x^2)^1/2

arcsinx+c

1/1+^2

arctanx+c

1/x(x^2-1)^1/2

arcsecx+c

1/x

ln /x/ +c

lnx

xlnx-x+c

tanx

ln/secx/+c

cotx

-ln/cscx/+c

secx

ln/secx+tanx/+c

cscx

-ln/cscx+cot/+c

integration by parts

fg'dx= fg- (integral)fg'dx

three pythagorians identities

sin^2 (x) +cos^2 (x) = 1


sec^2 (x) - tan^2 (x) = 1


csc^2 (x) - cot^2 (x) =1

sin(2x) =

sinxcosx

cos(2x)

cos^2(x)-sin^2x

if the sin's power is odd

u=cos x

if cos's power is odd

u=sinx

if both are even

use double angles

riemmans sum (3formulas)


important limit to know

double angle sin^2(x) =
(1-cos(2x))/2

double angle cos^2(x)

(cos(2x) +1)/2

a^2-x^2

x=asiny


dx=acos(y)dy


a^2-x^2 cos^2y

a^2+x^2

x=atany


a^2+x^2 = a^2sec^2(y)


dx= asec(y)tan(y)dy

x^2-a^2

x=asecx


dx=asecytanydy


a^2tan^2(y)