AP Calc - Advanced Integration Techniques Formulas

sin²x Identities

1. sin²x = 1-cos²x

2. sin²x = (1-cos2x)/2

cos²x Identities

1. cos²x = 1-sin²x

2. cos²x= (1+cos2x)/2

Integration by Parts Formula

∫u*dv = u*v - ∫v*dv

LIPET Acronym - Integration by Parts

Logarithmic, Inverse Trig, Polynomial, Exponential, Trogonometry

• Determines u

sec²x Identity

1. Sec²x = 1 + tan²x

2. Integral of secxdx = ln|secx+tanx| + C

tan²x Identity

1. tan²x = sec²x-1

2. Integral of tanxdx = -ln|cosx|+C

Trigonometric Substitution - sqrt(a²-u²)

1. x = a*sin(theta)

2. sqrt(a²-u²) = a*cos(theta)

Trigonometric Substitution - sqrt(a²+u²)

1. x = a*tan(theta)

2. sqrt(a²+u²) = a*sec(theta)

Trigonometric Substitution - sqrt(u²-a²)

1. x = a*sec(theta)

2. sqrt(u²-a²) = a*tan(theta)

d/dx(sinx)

cosx

d/dx(cosx)

-sinx

d/dx(tanx)

sec²x

d/dx(secx)

secxtanx

d/dx(cscx)

-cscxcotx

d/dx(cotx)

-csc²x