Calculus Examples

Since is constant with respect to , the integral of with respect to is .
Let . Then , so . Rewrite using and .
Combine fractions.
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Write as a fraction with denominator .
Multiply and .
Since is constant with respect to , the integral of with respect to is .
Simplify terms.
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Write as a fraction with denominator .
Multiply and .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Rewrite as .
By the Power Rule, the integral of with respect to is .
Simplify the answer.
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Write as a fraction with denominator .
Multiply and .
Simplify.
Write as a fraction with denominator .
Multiply and .
Multiply by .
Replace all occurrences of with .
Simplify each term.
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Factor.
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Apply the product rule to .
Remove unnecessary parentheses.
Move to the numerator using the negative exponent rule .
Multiply by by adding the exponents.
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Move .
Use the power rule to combine exponents.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
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