example of integration by parts involving algebraic manipulation
Using integration by parts with the substitutions
Using integration by parts on the integral on the right hand side with the substitutions
The “trick” is to add to both sides of the equation. Some people find this concept surprising at first sight, especially since most people who are taking calculus for the first time do not use equations when showing their work for integration. For integrals such as , writing out an equation is essential.
After adding to both sides of the above equation, we will need a on the right hand side. Thus, we obtain
Therefore, we can figure out what is by dividing both sides by , which yields
On the other hand, since is an arbitrary constant, we generally write
with the understanding that the constant in the final equation may not have the same value as appearing in equations in previous steps.
|Title||example of integration by parts involving algebraic manipulation|
|Date of creation||2013-03-22 17:39:52|
|Last modified on||2013-03-22 17:39:52|
|Last modified by||Wkbj79 (1863)|