MAT 21B Basic Integration Formulas/Trig formulas

∫dx/x

ln |x| +c

∫a^x dx

a^x/lna +c

∫sinx dx

-cosx +c

∫cosx dx

sinx +c

∫sec²x dx

tanx +c

∫csc²x dx

-cotx +c

∫secxtanx dx

secx +c

∫cscxcotx dx

-cscx +c

∫tanx dx

ln |secx| +c

∫cotx dx

ln |sinx| +c

∫secx dx

ln |secx + tanx| +c

∫cscx dx

-ln |cscx + cotx| +c

∫dx/√a²-x²

arcsin(x/a) +c

∫dx/a²+x²

1/a * arctan |x/a| +c

∫dx/x√x²-a².

1/a * arcsec |x/a| +c

Half-angle formula sin(x/2)

± √1-cosx/2

Half angle formula sin²x

(1-cos2x)/2

Half angle formula cos(x/2)

±√(1+cosx)/2

Half angle formula cos²x

(1+cos2x)/2

Half-angle formula tan(x/2)

• ± √(1-cosx)/1+cosx

• sinx/1+cosx

• 1-cosx/sinx

Double angle formula sin(2x)

2sinxcosx

Double angle formula cos(2x) #1

cos²xsin²x

Double angle formula cos(2x) #2

1-2sin²x

Double angle formula cos(2x) #3

2cos²x-1