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31 Cards in this Set
- Front
- Back
ad: x^n |
x^n+1/n+1+c |
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ad: sinx |
-cosx+c |
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ad: cosx
|
sinx+c |
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ad: sec^2x |
tanx+c |
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ad: csc^2 |
-cot x+c |
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ad: secxtanx |
secx+c |
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ad: e^x |
e^x+c |
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ad: a^x |
a^x/ln a +C |
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1/(1-x^2)^1/2 |
arcsinx+c |
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1/1+^2 |
arctanx+c |
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1/x(x^2-1)^1/2 |
arcsecx+c |
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1/x |
ln /x/ +c |
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lnx |
xlnx-x+c |
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tanx |
ln/secx/+c |
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cotx |
-ln/cscx/+c |
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secx |
ln/secx+tanx/+c |
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cscx
|
-ln/cscx+cot/+c |
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integration by parts |
fg'dx= fg- (integral)fg'dx |
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three pythagorians identities |
sin^2 (x) +cos^2 (x) = 1 sec^2 (x) - tan^2 (x) = 1 csc^2 (x) - cot^2 (x) =1 |
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sin(2x) = |
sinxcosx |
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cos(2x) |
cos^2(x)-sin^2x |
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if the sin's power is odd |
u=cos x |
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if cos's power is odd |
u=sinx |
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if both are even |
use double angles |
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riemmans sum (3formulas) |
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important limit to know |
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double angle sin^2(x) =
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(1-cos(2x))/2
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double angle cos^2(x) |
(cos(2x) +1)/2 |
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a^2-x^2 |
x=asiny dx=acos(y)dy a^2-x^2 cos^2y |
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a^2+x^2 |
x=atany a^2+x^2 = a^2sec^2(y) dx= asec(y)tan(y)dy |
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x^2-a^2 |
x=asecx dx=asecytanydy a^2tan^2(y) |