Worksheets · Calculus

Integration power rule worksheet

Integration undoes differentiation, so the power rule runs backwards: add one to the exponent and divide by what you just made. The constant of integration is there because differentiating loses it.

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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integration by the Power Rule

Date Period

Evaluate each integral.

  1. ∫216x5−196x6 dx
  2. ∫294x6+216x5 dx
  3. ∫−147x6−72x5 dx
  4. ∫49x6−72x5 dx
  5. ∫−36x5−294x6 dx
  6. ∫−49x6−144x5 dx
  7. ∫−49x6−216x5 dx
  8. ∫−144x5+98x6 dx
  9. ∫−72x5−245x6 dx
  10. ∫36x5+147x6 dx
  11. ∫98x6−144x5 dx
  12. ∫245x6−144x5 dx
  13. ∫−108x5−294x6 dx
  14. ∫−72x5+294x6 dx
  15. ∫98x6−36x5 dx
  16. ∫98x6−108x5 dx
  17. ∫180x5−147x6 dx
  18. ∫−147x6−108x5 dx
  19. ∫196x6+144x5 dx
  20. ∫180x5+294x6 dx

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integration by the Power RuleAnswer keyVersion 1

Date Period

Evaluate each integral.

  1. ∫216x5−196x6 dx36x6−28x7+C
  2. ∫294x6+216x5 dx42x7+36x6+C
  3. ∫−147x6−72x5 dx−21x7−12x6+C
  4. ∫49x6−72x5 dx7x7−12x6+C
  5. ∫−36x5−294x6 dx−6x6−42x7+C
  6. ∫−49x6−144x5 dx−7x7−24x6+C
  7. ∫−49x6−216x5 dx−7x7−36x6+C
  8. ∫−144x5+98x6 dx−24x6+14x7+C
  9. ∫−72x5−245x6 dx−12x6−35x7+C
  10. ∫36x5+147x6 dx6x6+21x7+C
  11. ∫98x6−144x5 dx14x7−24x6+C
  12. ∫245x6−144x5 dx35x7−24x6+C
  13. ∫−108x5−294x6 dx−18x6−42x7+C
  14. ∫−72x5+294x6 dx−12x6+42x7+C
  15. ∫98x6−36x5 dx14x7−6x6+C
  16. ∫98x6−108x5 dx14x7−18x6+C
  17. ∫180x5−147x6 dx30x6−21x7+C
  18. ∫−147x6−108x5 dx−21x7−18x6+C
  19. ∫196x6+144x5 dx28x7+24x6+C
  20. ∫180x5+294x6 dx30x6+42x7+C

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

∫6x2 dx

  1. The power goes from 2 to 3.
  2. Divide the 6 by the new power.
  3. And add C.

The answer is 2x3+C.

Where students go wrong

Leaving out the + C. It is not decoration: every constant differentiates to zero, so an indefinite integral without it names one antiderivative out of infinitely many.

Also called antiderivatives, indefinite integrals or reverse power rule.

Questions about these worksheets

Yes. Every integration power rule sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the integration power rule questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Leaving out the + C. It is not decoration: every constant differentiates to zero, so an indefinite integral without it names one antiderivative out of infinitely many.