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Calculus Examples
Step 1
Step 1.1
Let . Find .
Step 1.1.1
Differentiate .
Step 1.1.2
Differentiate using the Power Rule which states that is where .
Step 1.2
Rewrite the problem using and .
Step 2
Step 2.1
Rewrite as .
Step 2.1.1
Use to rewrite as .
Step 2.1.2
Apply the power rule and multiply exponents, .
Step 2.1.3
Combine and .
Step 2.1.4
Cancel the common factor of and .
Step 2.1.4.1
Factor out of .
Step 2.1.4.2
Cancel the common factors.
Step 2.1.4.2.1
Factor out of .
Step 2.1.4.2.2
Cancel the common factor.
Step 2.1.4.2.3
Rewrite the expression.
Step 2.1.4.2.4
Divide by .
Step 2.2
Rewrite as .
Step 2.2.1
Use to rewrite as .
Step 2.2.2
Apply the power rule and multiply exponents, .
Step 2.2.3
Combine and .
Step 2.2.4
Cancel the common factor of and .
Step 2.2.4.1
Factor out of .
Step 2.2.4.2
Cancel the common factors.
Step 2.2.4.2.1
Factor out of .
Step 2.2.4.2.2
Cancel the common factor.
Step 2.2.4.2.3
Rewrite the expression.
Step 2.2.4.2.4
Divide by .
Step 2.3
Combine and .
Step 2.4
Combine and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Step 4.1
Let . Find .
Step 4.1.1
Differentiate .
Step 4.1.2
Differentiate using the Power Rule which states that is where .
Step 4.2
Rewrite the problem using and .
Step 5
Combine and .
Step 6
Since is constant with respect to , move out of the integral.
Step 7
Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 8
The integral of with respect to is .
Step 9
Simplify.
Step 10
Step 10.1
Replace all occurrences of with .
Step 10.2
Replace all occurrences of with .