Calculus
Power, Constant, and Sum Rules worksheets
Differentiate constants, polynomial sums, reciprocal monomials, and exact rational powers with the original real-domain conditions preserved.
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Power Rule Integration worksheets
Find exact indefinite integrals of polynomial, reciprocal integer-power, and reciprocal rational-power functions while preserving the original real domain.
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Find each indefinite integral. Give an exact antiderivative and include + C.
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Customize this worksheetIntegrate exact powers
Rewrite reciprocal expressions as negative powers, apply the Power Rule term by term, and include one arbitrary constant.
Learning objective
What this activity builds
Apply the Power Rule for integration to exact one-variable terms and include the arbitrary constant.
Worked example
Find the indefinite integral of 6x².
2x³ + C
Increase the exponent from 2 to 3, then divide the coefficient 6 by 3.
Teaching notes
Make the practice count
- Rewrite reciprocals as negative powers.
- Increase the exponent by one before dividing the coefficient.
- Keep + C and the original domain restriction.
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Differentiate exact powers of polynomial binomials and square roots of odd polynomial powers, keeping each answer in concise factored form.
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