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:

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.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: