1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 8x − 4/x(x2 + 1)2
2. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
2x3 - 16x2 - 39x + 20/x2 - 8x - 20 x dx
3. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
x2/x4 - 42x2 - 343 x dx

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

2.

Using partial fraction decomposition to find the definite integral of:

By using the long division method; we have:

So;

By using partial fraction decomposition:

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now;  we have to relate like terms on both sides; we have:

A + B = 1   ;   2A - 10 B = 20

By solvong the expressions above; we have:

Now;

Thus;

Now; the integral is:

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

56

step-by-step explanation: