Is there a better way to integrate this

  • Thread starter Dell
  • Start date
  • #1
590
0
what is the best way to integrate this functio, i integrated in parts

f(x)=x2/2x+3


i split the top of the fraction and then integrated the x2 half using integration in parts, but its just long and lots of place to make mistakes.
 

Answers and Replies

  • #2
283
3
I would try to rid of the top bit. Here is a hint [tex] x^2=\frac{1}{4}((2x-3)(2x+3) + 9) [/tex].

Good luck
 
  • #3
jambaugh
Science Advisor
Insights Author
Gold Member
2,279
295
what is the best way to integrate this functio, i integrated in parts

f(x)=x2/2x+3


i split the top of the fraction and then integrated the x2 half using integration in parts, but its just long and lots of place to make mistakes.

I assume you mean:
[tex]\frac{x^2}{2x+3}[/tex]

Note the degree of the numerator is higher than that of the denominator. (Improper rational function like an improper fraction.)
You should first carryout long division of the polynomials (and check by re-multiplying).
You will then get a polynomial plus a proper fraction. Since the denom. has degree 1 the numerator (remainder) will be constant and you can integrate via simple variable substitution.

Carry out the long division:
[tex] 2x+3)\overline{x^2 + 0x + 0}[/tex]

You should get:
[tex] P(x)+ \frac{C}{2x+3}[/tex]
where P is a polynomial

You can easily integrate:
[tex] \int P(x)dx + C/2 \int \frac{du}{u};\quad u = 2x+3[/tex]
 

Related Threads on Is there a better way to integrate this

Replies
25
Views
3K
Replies
4
Views
1K
Replies
5
Views
614
Replies
5
Views
1K
Replies
30
Views
2K
Replies
11
Views
1K
Replies
6
Views
1K
Replies
6
Views
1K
Replies
3
Views
5K
Top