(adsbygoogle = window.adsbygoogle || []).push({}); 1. ∫[itex]\frac{dx}{x^{3}+ 2x}[/itex]

We're suppose to evaluate the integral.

Use Partial Fraction Decomposition:

[itex]\frac{1}{x^{3}+ 2x}[/itex] = [itex]\frac{A}{x}[/itex] + [itex]\frac{Bx + C}{x^{2}+ 2}[/itex]

1 = A(x^{2}+ 2) + (Bx + C)(x)

1 = Ax^{2}+ 2A + Bx^{2}+ Cx

1 = x^{2}( A + B) + Cx + 2A

Solving for A gives [itex]\frac{1}{2}[/itex]

Solving for B gives -[itex]\frac{1}{2}[/itex]

Solving for C gives 0

∫[itex]\frac{dx}{x(x^{2}+ 2}[/itex] = [itex]\frac{1}{2}[/itex]∫[itex]\frac{dx}{x}[/itex] - [itex]\frac{1}{2}[/itex]∫[itex]\frac{dx}{x^{2}+ 2}[/itex]

When we evaluate this, I get:

[itex]\frac{1}{2}[/itex]ln x - [itex]\frac{1}{2}[/itex]tan^{-1}[itex]\frac{x}{\sqrt{2}}[/itex]

Or should it be:

[itex]\frac{1}{2}[/itex]ln x - [itex]\frac{1}{2}[/itex]ln (x^{2}+ 2)

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# Homework Help: Integrating Rational Functions

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