Question

When integrating a challenging expression, what is the first step to make it suitable for substitution?

a) Complete the square
b) Factorize the expression
c) Split the two terms into two integrals
d) Simplify the expression by bringing out multiplying constants

Answer 1

The first step in integrating a complex expression is to simplify it by eliminating terms, which could include factoring or bringing out constants. Then, look for a suitable substitution to facilitate integration. Finally, check the answer for reasonableness.

Step-by-step explanation:

When integrating a challenging expression, the first step to make it suitable for substitution is typically to simplify the expression by eliminating terms wherever possible. This may involve factoring the expression, combining like terms, or bringing out multiplying constants. Once simplified, this can make it easier to spot a suitable substitution that will make the integral more manageable. After the integral is performed, always check the answer to ensure it is reasonable, and don't forget to reverse the substitution if necessary.