Other Strategies for Integration

The strategic overview

Algebraic preprocessing

Integral tables and computer algebra

When no elementary antiderivative exists

An integrand is a rational function, a ratio of polynomials. Which technique is designed for it?

Which algebraic step unlocks the integral of (x^2 + 1)/x dx?

Which integral has no elementary antiderivative?

The integral of dx/(1 + sqrt(x)) is unlocked by which substitution?

The trick for integrating sec x multiplies by (sec x + tan x) over itself. What does this manufacture?

Before computer algebra, working integrators consulted printed collections of standard antiderivatives. As two words, what were these called? Answer like answer keys.

Computer algebra systems integrate instantly. Why does the course still teach the manual techniques?

The error function erf(x) is defined by an integral of e^(-t^2). Since no elementary antiderivative exists, erf is an example of what kind of function? Answer with two words.

Computer algebra systems apply the full integration decision procedure automatically. As a three-letter abbreviation, what are these systems called? Answer in lowercase.

In the diagnostic order, the first technique to try for an unfamiliar integrand is which one, named after the chain rule's reversal? Answer with one word.