Cloned from: Calculus Integrals



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∫xndx
xn+1 + C
¯¯¯¯
n+1
du
¯¯¯¯
u
ln lul + C
∫eudu
eu + C
∫sin u du
-cos u + C
∫cos u du
sin u + C
∫tan u du
ln lsec ul + C
∫ du
————
a2+u2
1/a arctan u/a + C
∫cot u du
ln |sin u| + C
∫sec u du
ln |sec u + tan u| + C
∫csc u du
-ln |csc u + cot u| + C
∫sec2 u du
tan u + C
∫csc2 u du
-cot u + C
∫sec u tan u du
sec u + C
∫csc u cot u du
-csc u + C
∫ du
————
√a2-u2
arcsin u/a + C
∫ du
————
u √a2-u2
1/a arcsec |u|/a + C
sin 2u
2sin u cos u
sin2 u
1 - cos 2u
————
2
tan2u
1 - cos 2u
————— 
1 + cos 2u
if secant is odd and positive with no tangents
integrate by parts
∫ u dv =
uv - ∫ v du
if secant is even and positive
save secant2 and convert the rest to tangents
if tangent is odd and positive
save secant tangent, and convert the rest to secants
if sin is odd and positive
save one sine and convert the rest to cosine
if cosine is odd and positive
save one cosine and convert the rest to sine
if both cosine and sine are even and positive
use power reducing formulas
1 + tan2x =
sec2x
√a2-u2
u=a sinΘ
u is opposite
a is hypotenuse
√u2-a2
u = a sec Θ
u is hypotenuse
a is adjacent
√a2+u2
u = a tan Θ
u is opposite
a is adjacent
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