Help. I have a test! Improper fraction integration of

Question

∫ (x^3 - 7x^2 + 5x + 40) / (x^2 - 2x - 8) dx Thank you?

Answer 1

Step 1:

The integral expression is .

Simplify the integrand by using long division.

Result of long division is .

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Step 2:

Partial decomposition of .

Equate the coefficients.

Equate the constant terms.

Multiply each side of equation by .

Add the equations and .

Substitute in equation .

Substitute the values , in equation .

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Step 3:

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Solution:

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