# Integration by Partial Fractions: Example 5

In this video I go over another example on integration of rational functions by partial fractions and this time integrate a function that has a non-reducible non-linear factor in the denominator. This requires applying the method of partial fraction decomposition but for non-linear factors as I have shown in my earlier videos and you can see those in the links below. The example I go over is the integral of (2x^2 – x + 4)/(x^3 + 4x). In the example I derive the integral of 1/(x^2 + a^2) = 1/a * inverse tan (x/a) which was required in solving the overall integral.

Related Videos:

Integration by Partial Fractions: Example 4: http://youtu.be/79lWkqMEzUU

Integration by Partial Fractions: Example 3: http://youtu.be/Ch2qP4uqluc
Corollary of Continuity Theorem: Proof: http://youtu.be/euAJAiFdIAA
Integration by Partial Fractions: Example 2: http://youtu.be/Fi16rcXUxHo
Integration by Partial Fractions: Example 1: http://youtu.be/UZthT_bCKyU
Integration by Partial Fractions: http://youtu.be/r07NnKf76og
Partial Fraction Decomposition: Summary and Higher Powers: http://youtu.be/lSlkhrF09ww
Partial Fraction Decomposition: Proof of General Case with Linear Factors: https://youtu.be/crTTU9SpTNI
Partial Fraction Decomposition: Proof of the Simplest Case: http://youtu.be/Eq5yLJmC6pw
Partial Fraction Decomposition: Why it doesn’t for Improper Fractions: http://youtu.be/5QQP2kqE_ss
Partial Fraction Decomposition: Non-Linear and Repeating Factors: http://youtu.be/wZVI5Gsc4WU
Partial Fraction Decomposition: Non-Linear Factors: http://youtu.be/ZK8akA4BE84
Partial Fraction Decomposition: Repeating Factors: http://youtu.be/9xlyx5NumkI
Partial Fraction Decomposition: General Techniques: http://youtu.be/bqf42x6nZoo
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
Derivative of y = Log(x) and y = Ln(x): http://youtu.be/5e6MisvvMP Polynomial Long Division – Examples: http://youtu.be/7XbzCQgqBPc
Derivative of arctan(x) or Inverse tan(x): http://youtu.be/q9jdOiQ7pZY .

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