## mathematics44 2 years ago Integrate (x+3)/(x-7)^2 using partial integration method?

1. .Sam.

Partial fractions?

2. .Sam.

$\frac{3+x}{(x-7)^2}=\frac{A}{x-7}+\frac{B}{(x-7)^2}$

3. mathematics44

Yeah, it was partial fractions. My bad. lol

4. .Sam.

So did you get it?

5. mathematics44

I knew how to do it up until this point but if you plug in 7, it gives you A(0) + B(0) = 10, so how do I find out the values of A and B separately?

6. SithsAndGiggles

Try values other than 7. Like x = 1 and 0, for convenience. This should give you a system of two equations with the unknowns, A and B.

7. mathematics44

I tried 6 and 8 and answer that I got is A=10 , B= 1. I hope that's correct

8. .Sam.

$x+3=B+A (x-7)$ When x=7 B=10 When B has this value, when x=0, 0+3=10-7A A=1 $\frac{x+3}{(x-7)^2}=\frac{1}{x-7}+\frac{10}{(x-7)^2}$

9. .Sam.

Can you do it now? $\int\limits \left(\frac{10}{(x-7)^2}+\frac{1}{x-7}\right) \, dx$

10. mathematics44

yes. thank you for your help