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Calculus Examples
Step 1
Let , where . Then . Note that since , is positive.
Step 2
Step 2.1
Simplify .
Step 2.1.1
Simplify each term.
Step 2.1.1.1
Apply the product rule to .
Step 2.1.1.2
Raise to the power of .
Step 2.1.2
Factor out of .
Step 2.1.2.1
Factor out of .
Step 2.1.2.2
Factor out of .
Step 2.1.2.3
Factor out of .
Step 2.1.3
Apply pythagorean identity.
Step 2.1.4
Rewrite as .
Step 2.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2
Cancel the common factor of .
Step 2.2.1
Factor out of .
Step 2.2.2
Cancel the common factor.
Step 2.2.3
Rewrite the expression.
Step 3
The integral of with respect to is .
Step 4
Replace all occurrences of with .
Step 5
Reorder terms.