Integrating Using Partial Fractions when the Denominator Contains Irreducible Quadratic Factors
The Riemann Sum Formula For the Definite Integral
The Sum Rule, the Constant Multiple Rule, and the Power Rule for Integration

Integration by Parts Problems where You Go around in Circles

Sometimes if you use integration by parts twice, you get back to where you started from — which, unlike getting lost, is not a waste of time.

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First, use the LIATE mnemonic device to pick your u:

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To pick your u, go down this list in order; the first type of function on this list that appears in the integrand is the u.

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Now fast forward to the formula step:

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Now, substitute the right side of the above equation for the

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from the original solution:

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You can now solve this equation for the integral

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Use I in place of that integral to make this messy equation easier on the eyes:

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Add I to both sides:

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Multiply both sides by 1/2:

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Integrate Functions Where the Denominator Contains Irreducible Quadratic Factors
The Fundamental Theorem of Calculus
How to Use Sigma Notation
How to Find Antiderivatives by Guessing and Checking
How to Solve Integrals Using Integration by Parts
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