Math 22 - Integration Techniques (with some Math 20-21 recap)

Integration by Parts (IBP) Formula

LIATE for IBP

L − logarithmic function

I − inverse trigonometric function

A − algebraic function

T − trigonometric function

E − exponential function

Integrating Powers of Sines and Cosines

Integrating Products of Sines and Cosines

Integrating Powers of Tangents and Cotangents

Integrating Powers of Secants and Cosecants

Integrating Products of Tangents and Secants or Cotangents and Cosecants

Product-to-Sum Trigonometric Identities

Integrand contains √(a²-u²)

u = a sin θ

du = a cos θ dθ

√(a²-u²) = a cos θ

Integrand contains √(u²-a²)

u = a sec θ

du = a sec θ tan θ dθ

√(u²-a²) = a tan θ

Integrand contains √(u²+a²)

u = a tan θ

du = a sec² θ dθ

√(u²+a²) = a sec θ

Partial Fractions: The denominator has distinct linear factors.

Partial Fractions: The denominator has repeated linear factors.

Partial Fractions: The denominator has an irreducible quadratic factor.

Partial Fractions: The denominator has a repeated irreducible quadratic factor.

Derivatives of Inverse Trigonometric Functions

Derivatives of Inverse Hyperbolic Functions

Antiderivatives Yielding the Inverse Circular Functions

Antiderivatives of Hyperbolic Functions (tanh, coth, sech, csch)

Antiderivatives of Trigonometric Functions (tan, cot, sec, csc)

Negative Angles (Even/Odd Identities)

Pythagorean Identities

Double-Angle Identities

Half-Angle Identities