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Calculus Examples
Step 1
Step 1.1
Divide each term in by .
Step 1.2
Cancel the common factor of .
Step 1.2.1
Cancel the common factor.
Step 1.2.2
Divide by .
Step 1.3
Factor out of .
Step 1.4
Reorder and .
Step 2
Step 2.1
Set up the integration.
Step 2.2
Integrate .
Step 2.2.1
Since is constant with respect to , move out of the integral.
Step 2.2.2
The integral of with respect to is .
Step 2.2.3
Simplify.
Step 2.3
Remove the constant of integration.
Step 2.4
Use the logarithmic power rule.
Step 2.5
Exponentiation and log are inverse functions.
Step 3
Step 3.1
Multiply each term by .
Step 3.2
Simplify each term.
Step 3.2.1
Combine and .
Step 3.2.2
Cancel the common factor of .
Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factor.
Step 3.2.2.3
Rewrite the expression.
Step 3.2.3
Rewrite using the commutative property of multiplication.
Step 3.3
Cancel the common factor of .
Step 3.3.1
Factor out of .
Step 3.3.2
Cancel the common factor.
Step 3.3.3
Rewrite the expression.
Step 4
Rewrite the left side as a result of differentiating a product.
Step 5
Set up an integral on each side.
Step 6
Integrate the left side.
Step 7
Step 7.1
Integrate by parts using the formula , where and .
Step 7.2
Since is constant with respect to , move out of the integral.
Step 7.3
Simplify.
Step 7.3.1
Multiply by .
Step 7.3.2
Multiply by .
Step 7.4
The integral of with respect to is .
Step 7.5
Rewrite as .
Step 8
Step 8.1
Divide each term in by .
Step 8.2
Simplify the left side.
Step 8.2.1
Cancel the common factor of .
Step 8.2.1.1
Cancel the common factor.
Step 8.2.1.2
Divide by .
Step 8.3
Simplify the right side.
Step 8.3.1
Simplify each term.
Step 8.3.1.1
Cancel the common factor of and .
Step 8.3.1.1.1
Factor out of .
Step 8.3.1.1.2
Cancel the common factors.
Step 8.3.1.1.2.1
Factor out of .
Step 8.3.1.1.2.2
Cancel the common factor.
Step 8.3.1.1.2.3
Rewrite the expression.
Step 8.3.1.2
Move the negative in front of the fraction.