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Sin²x+Cos²x
=1
1 + tan²x
=sec²x
cot²x+1
=csc²x
sin2x
=2sinxcosx
Sinx + cosx
=1/2 sin(2x)
cos2x
=cos²x-sin²x
sin²x
=(1-cos2x)/2
cos²x
=(1+cos2x)/2
√(a²-x²)
x = asinΘ
cos²Θ=1-sin²Θ
√(a²+x²)
x=atanΘ
sec²Θ=1+tan²Θ
√(x²-a²)
x=asecΘ
tan²Θ=sec²Θ-1
∫sinudu
= -cosu + C
∫cosudu
= sin u + C
∫tanudu
= -ln|cosu| + C
∫cscudu
= -ln|cscu + cotu| + C
∫secudu
= ln|secu + tanu| + C
∫cotudu
= ln|sinu| + C
∫e^u du
= e^u + C
∫1/u du
= ln|u| + C
∫a^u du
= (a^u)/lna + C
∫1/(1+x²)dx
= arctanx + C
∫1/√(1-x²)dx
= arcsinx + C
∫-1/√(1-x²)dx
= arccosx + C
∫1/(a²+u²)du
= 1/a(arctan(u/a)) + C
∫1/√(a²-u²)du
= arcsin(u/a) + C
∫1/(u√(u²-a²))
= 1/a(arcsec(|u|/a) + C