Enter a problem...
Calculus Examples
Step 1
Integrate by parts using the formula , where and .
Step 2
Step 2.1
Combine and .
Step 2.2
Combine and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Combine and .
Step 5
Integrate by parts using the formula , where and .
Step 6
Step 6.1
Combine and .
Step 6.2
Combine and .
Step 6.3
Combine and .
Step 6.4
Combine and .
Step 6.5
Combine and .
Step 6.6
Cancel the common factor of .
Step 6.6.1
Cancel the common factor.
Step 6.6.2
Divide by .
Step 7
Integrate by parts using the formula , where and .
Step 8
Step 8.1
Combine and .
Step 8.2
Combine and .
Step 8.3
Combine and .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
Step 10.1
Let . Find .
Step 10.1.1
Differentiate .
Step 10.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 10.1.3
Differentiate using the Power Rule which states that is where .
Step 10.1.4
Multiply by .
Step 10.2
Rewrite the problem using and .
Step 11
Combine and .
Step 12
Since is constant with respect to , move out of the integral.
Step 13
Step 13.1
Multiply by .
Step 13.2
Multiply by .
Step 14
The integral of with respect to is .
Step 15
Step 15.1
Rewrite as .
Step 15.2
Simplify.
Step 15.2.1
To write as a fraction with a common denominator, multiply by .
Step 15.2.2
Combine and .
Step 15.2.3
Combine the numerators over the common denominator.
Step 15.2.4
Multiply by .
Step 15.2.5
Combine and .
Step 15.2.6
Multiply by .
Step 15.2.7
Cancel the common factor of and .
Step 15.2.7.1
Factor out of .
Step 15.2.7.2
Cancel the common factors.
Step 15.2.7.2.1
Factor out of .
Step 15.2.7.2.2
Cancel the common factor.
Step 15.2.7.2.3
Rewrite the expression.
Step 15.2.7.2.4
Divide by .
Step 16
Replace all occurrences of with .
Step 17
Reorder terms.