Enter a problem...
Calculus Examples
Step 1
Split up the integral depending on where is positive and negative.
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Combine and .
Step 6
Apply the constant rule.
Step 7
Split the single integral into multiple integrals.
Step 8
Since is constant with respect to , move out of the integral.
Step 9
By the Power Rule, the integral of with respect to is .
Step 10
Combine and .
Step 11
Apply the constant rule.
Step 12
Step 12.1
Substitute and simplify.
Step 12.1.1
Evaluate at and at .
Step 12.1.2
Evaluate at and at .
Step 12.1.3
Evaluate at and at .
Step 12.1.4
Evaluate at and at .
Step 12.1.5
Simplify.
Step 12.1.5.1
Raising to any positive power yields .
Step 12.1.5.2
Cancel the common factor of and .
Step 12.1.5.2.1
Factor out of .
Step 12.1.5.2.2
Cancel the common factors.
Step 12.1.5.2.2.1
Factor out of .
Step 12.1.5.2.2.2
Cancel the common factor.
Step 12.1.5.2.2.3
Rewrite the expression.
Step 12.1.5.2.2.4
Divide by .
Step 12.1.5.3
Multiply by .
Step 12.1.5.4
Add and .
Step 12.1.5.5
Combine and .
Step 12.1.5.6
Multiply by .
Step 12.1.5.7
Multiply by .
Step 12.1.5.8
Add and .
Step 12.1.5.9
Raise to the power of .
Step 12.1.5.10
To write as a fraction with a common denominator, multiply by .
Step 12.1.5.11
Combine and .
Step 12.1.5.12
Combine the numerators over the common denominator.
Step 12.1.5.13
Multiply by .
Step 12.1.5.14
Multiply by .
Step 12.1.5.15
Combine and .
Step 12.1.5.16
Multiply by .
Step 12.1.5.17
To write as a fraction with a common denominator, multiply by .
Step 12.1.5.18
Combine and .
Step 12.1.5.19
Combine the numerators over the common denominator.
Step 12.1.5.20
Simplify the numerator.
Step 12.1.5.20.1
Multiply by .
Step 12.1.5.20.2
Add and .
Step 12.1.5.21
Move the negative in front of the fraction.
Step 12.2
Simplify.
Step 12.2.1
Combine the numerators over the common denominator.
Step 12.2.2
Simplify each term.
Step 12.2.2.1
Combine the numerators over the common denominator.
Step 12.2.2.2
Simplify each term.
Step 12.2.2.2.1
Apply the product rule to .
Step 12.2.2.2.2
Raise to the power of .
Step 12.2.2.2.3
Raise to the power of .
Step 12.2.2.3
To write as a fraction with a common denominator, multiply by .
Step 12.2.2.4
Combine and .
Step 12.2.2.5
Combine the numerators over the common denominator.
Step 12.2.2.6
Simplify the numerator.
Step 12.2.2.6.1
Multiply by .
Step 12.2.2.6.2
Subtract from .
Step 12.2.2.7
Cancel the common factor of .
Step 12.2.2.7.1
Factor out of .
Step 12.2.2.7.2
Cancel the common factor.
Step 12.2.2.7.3
Rewrite the expression.
Step 12.2.2.8
Combine and .
Step 12.2.2.9
Multiply by .
Step 12.2.2.10
Cancel the common factor of and .
Step 12.2.2.10.1
Factor out of .
Step 12.2.2.10.2
Cancel the common factors.
Step 12.2.2.10.2.1
Factor out of .
Step 12.2.2.10.2.2
Cancel the common factor.
Step 12.2.2.10.2.3
Rewrite the expression.
Step 12.2.3
Find the common denominator.
Step 12.2.3.1
Write as a fraction with denominator .
Step 12.2.3.2
Multiply by .
Step 12.2.3.3
Multiply by .
Step 12.2.3.4
Write as a fraction with denominator .
Step 12.2.3.5
Multiply by .
Step 12.2.3.6
Multiply by .
Step 12.2.4
Combine the numerators over the common denominator.
Step 12.2.5
Simplify each term.
Step 12.2.5.1
Multiply by .
Step 12.2.5.2
Multiply by .
Step 12.2.6
Add and .
Step 12.2.7
Subtract from .
Step 12.2.8
Simplify each term.
Step 12.2.8.1
Cancel the common factor of .
Step 12.2.8.1.1
Factor out of .
Step 12.2.8.1.2
Cancel the common factor.
Step 12.2.8.1.3
Rewrite the expression.
Step 12.2.8.2
Apply the product rule to .
Step 12.2.8.3
Raise to the power of .
Step 12.2.8.4
Raise to the power of .
Step 12.2.8.5
Multiply the numerator by the reciprocal of the denominator.
Step 12.2.8.6
Multiply .
Step 12.2.8.6.1
Multiply by .
Step 12.2.8.6.2
Multiply by .
Step 12.2.9
Combine the numerators over the common denominator.
Step 12.2.10
Add and .
Step 12.2.11
Cancel the common factor of and .
Step 12.2.11.1
Factor out of .
Step 12.2.11.2
Cancel the common factors.
Step 12.2.11.2.1
Factor out of .
Step 12.2.11.2.2
Cancel the common factor.
Step 12.2.11.2.3
Rewrite the expression.
Step 13
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Step 14