Calculus II

Express the integrated as a sum of partial fractions and evaluate the integral

3x2+x+9/(x2+5)(x-6)

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1. The partial fractions part come to:

(3x2+x+9)/((x2+5)(x-6))
= 3/(x-6) + 1/(x^2+5)

both of those are easy to integrate, right?

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2. We must be careful to insert parentheses when they are needed.
Expressions are evaluated according to the PEMDAS rule.
http://www.purplemath.com/modules/orderops.htm

For example, what you posted is mathematically equivalent

3x²+x +[9/(x²+5)]*(x-6)
which is (probably) not what you meant.

Correctly written, what you (probably) meant should read:

(3x2+x+9)/((x2+5)(x-6))

Here, we try to interpret correctly by guessing from context, but calculators are unforgiving with missing parentheses, that is why we need to develop the proper reflex for them.

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posted by MathMate

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