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x²+a² goes to
x = atan(theta)
a²-x² goes to
x = asin(theta)
x²-a² goes to
x = asec(theta)
cos²x+sin²x
=1
tan²x+1
=sec²x
sin(2x)
=2sin(x)cos(x)
cos²x
=½ +1/2cos(2x)
sin²x
=1/2-1/2cos(2x)
integral secx dx
= ln |secx + tanx| +C
integral secxtanx dx
= secx + C
integral cscxcotx dx
=-cscx + C
integral csc²x dx
= -cotx + C