Conceptual Integration by Parts problem

[Jaskaran]

Can be broken as

How do I solve for A and B ?!! :?

 

[Deleted member 4993]

Can be broken as

How do I solve for A and B ?!! :?

x[sup:239zvrgy]2[/sup:239zvrgy] + 3x - 40 ? factorize it then use "partial fraction" techniques or technology (as using a CAS calculator)

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[galactus]

If you factor the denominator, you get

$\displaystyle (x-5)(x+8)$

This can then be expanded into Partial fractions:

$\displaystyle \frac{A}{x-5}+\frac{B}{x+8}=10x-102$

$\displaystyle A(x+8)+B(x-5)=10x-102$

Distribute to eliminate parentheses on the left, equate coefficients, and solve for A and B.

You can also do partial fractions by subbing in the value of x that makes x+8=0

Then, sub in the value that makes x-5=0.

Some prefer this method over the other.

For instance, if x=-8:

$\displaystyle A(-8+8)+B(-8-5)=10(-8)-102$

There. You have B.

Do the same for A and you have it.

 

[Raven66]

Looks like that this problem is more related to integration of rational functions, not integration by parts. See some other typical examples at http://www.math24.net/integration-of-rational-functions.html.