Guide to choosing a method

Signal

Composition and the inner derivative appears

Method

Substitution

Signal

Product with logarithm, inverse trigonometric, or algebraic power

Method

Integration by parts

Signal

Powers of sine and cosine

Method

Identities and parity rules

Signal

Powers of tangent and secant

Method

Reserve ${\sec }^{2}x$ or $\sec x\tan x$

Signal

Quotient of polynomials

Method

Division and partial fractions

Signal

$\sqrt{a^2-x^2}$, $\sqrt{a^2+x^2}$, $\sqrt{x^2-a^2}$

Method

Trigonometric substitution

Signal

Non-standard quadratic inside a radical or denominator

Method

Completing the square

Signal

Infinite limits or singularities

Method

Improper integral using limits

Signal

Difficult antiderivative or tabulated data

Method

Numerical integration

Signal

Integrand with a recurring parameter

Method

Reduction formula