Download Strategy for integration

Strategy for integration.
1. Use a pencil. It helps to be able to erase.
If you do not immediately see how to attack an integral, you might try the following.
2. Simplify the integrand. This could mean using an algebraic manipulation or a
trigonometric identity.
3. Look for a u-substitution. Do not forget about u-substitution. This is usually
easier than using one of the other methods we have learned.
4. Classify the integral according to its form. Assume f(x) is the integrand.
a. Trigonometric functions: If f(x) is a product of powers of sin(x) and
cos(x) or tan (x) and sec (x) apply the methods of section 9.2. If it is not
in these terms, you could try rewriting in terms of sin x and cos x and see
if that helps.
b. Rational functions. If f(x) is a rational function and the denominator
factors, try partial fractions, section 9.3. If the denominator does not
factor, it is possible that a trig substitution could be used or that
completing the square followed by a trig substitution could be used.
c. If f(x) is a product of two functions then you could try integration by parts,
see section 9.1.
d. If f(x) contains a radical:
i. square root – try a trig substitution, possible requiring completing
the square first.
ii. any other radical – try a rationalizing substitution.
5. If the method you tried does not work, erase and try something else. Sometimes
the seemingly obvious way, is not the way to solve an integral
Notes: You will get better with experience, there is no substitute. The best way to learn
to do this is to put away the answer book and complete the random integrals in section
9.8. It will take a long time, but it is the only way I know of to learn this.