Use trigonometric substitution to find the following integral. integral {(x - 3)^3} / {square...

Question:

Use trigonometric substitution to find the following integral.

{eq}\displaystyle \int \dfrac {(x - 3)^3} {\sqrt {x^2 - 6 x}}\ dx {/eq}

Trigonometric Substitution:

Trigonometric substitution is used to solve definite integrals that contain sum and differences of squares where one of the terms is a function of the independent variable. A variable change is introduced that involves a trigonometric function, the integral is solved and finally, identities are used to return to the original variable.

Answer and Explanation: 1

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To solve the following integral

{eq}\displaystyle \int \dfrac{(x-3)^3}{\sqrt{x^2 - 6x}}dx \\ {/eq}

Initially squares are completed in the...

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Understanding Trigonometric Substitution

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Chapter 13 / Lesson 11
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What is trig substitution for integrals? See examples to understand integration by trigonometric substitution using the three trig substitution identities.


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