If necessary, use two or more substitutions to find the following integral. dx (Hint: Begin withu= /6+x.) 17+ v6+x

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Author:James Stewart
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Chapter1: Functions And Models
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### Exercise 5.5.117

**Objective:**
Use substitution techniques to find the following integral. If necessary, perform two or more substitutions.

**Integral to Evaluate:**

\[
\int \frac{dx}{\sqrt{7 + \sqrt{6 + x}}}
\]

**Hint:**
Begin with the substitution \( u = \sqrt{6 + x} \).

**Solution Box:**

\[
\int \frac{dx}{\sqrt{7 + \sqrt{6 + x}}} = \boxed{\phantom{1}}
\]

**Note:**
Type an exact answer, using radicals as needed.
Transcribed Image Text:### Exercise 5.5.117 **Objective:** Use substitution techniques to find the following integral. If necessary, perform two or more substitutions. **Integral to Evaluate:** \[ \int \frac{dx}{\sqrt{7 + \sqrt{6 + x}}} \] **Hint:** Begin with the substitution \( u = \sqrt{6 + x} \). **Solution Box:** \[ \int \frac{dx}{\sqrt{7 + \sqrt{6 + x}}} = \boxed{\phantom{1}} \] **Note:** Type an exact answer, using radicals as needed.
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