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

Question

.sam. · Answer

Partial fractions?

.sam. · Answer

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

anonymous · Answer

Yeah, it was partial fractions. My bad. lol

.sam. · Answer

So did you get it?

anonymous · Answer

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?

anonymous · Answer

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.

anonymous · Answer

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

.sam. · Answer

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

.sam. · Answer

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

anonymous · Answer

yes. thank you for your help