Differential Equations For Dummies
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With the trigonometric substitution method, you can do integrals containing radicals of certain forms because they match up with trigonometric functions. A sine can take the place of a radical in a particular form.

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  1. Draw a right triangle where

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    You should confirm this with the Pythagorean theorem.

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  2. Solve

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    differentiate, and solve for dx.

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  3. Find which trig function equals the radical over the a, and then solve for the radical.

    Look at the triangle in the figure.

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  4. Use the results from Steps 2 and 3 to make substitutions in the original problem and then integrate.

    Note that in this particular problem, you have to make three substitutions, not just two like in the first example.

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  5. The triangle shows that

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    Now, substitute back for your final answer.

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It’s a walk in the park.

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