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integral of f(x)±g(x) dx
integral of f(x) dx ± integral of g(x) dx
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integral of f(x)^n f'(x) dx
[f(x)]^n+1/n+1 + C
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integral of cos(x)
sin(x)
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integral of sin(x)
-cos(x)
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integral of sec^2(x)
tan(x)
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integral of csc^2(x)
-cot(x)
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integral of sec(x)tan(x)
sec(x)
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integral of -csc(x)cot(x)
csc(x)
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integral of 1/f(x) dx
ln|f(x)|
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integral of b^f(x)
1/lnb ⋅ b^f(x)
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integral of 1/[sqrt of a^2-f(x)^2] dx
arcsin (f(x)/a)
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integral of 1/[a^2+f(x)^2]
1/a arctan(f(x)/a)
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integral of 1/|f(x)|[sqrt of f(x)^2 - a^2] dx
1/a arcsec(f(x)/a)
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integral of tan(f(x))
-ln|cos(f(x))| + C
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integral of cot(f(x))
ln|sin(f(x))| + C
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integral of sec(f(x))
ln|sec(f(x))+tan(f(x))| + C
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integral of csc(f(x))
ln|csc(f(x))-cot(f(x))| + C
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What to do when have 1 odd trig function and an even one
take one out of the odd then make everything the opposite of what the taken out one was
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what to do with one even function
use x many half angle formulas
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What to do when one trig function is a square root and one is even
split the even one using pythagorean identities
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What to do with one odd trig function
take one out and use pythagorean identities
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what to do with mismatched functions (not related to each other)
turn into their sin/cos versions and solve
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What are the three pythagorean identities?
- sin^2x + cos^2x = 1
- 1 + tan^2x = sec^2x
- 1 + cot^2x = csc^2x
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Half angle formula for sin
[1-cos(2x)]/2
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half angle formula for cos
[1+cos(2x)]/2
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range for arcsin
[-pi/2, pi/2], where y= the sin value given
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range for arccos
[0, pi], where y= cos value given
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range for arctan
(-pi/2, pi/2), where the value= y/x
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