Worksheet: Indefinite Integrals: The Power Rule

In this worksheet, we will practice finding the indefinite integrals of polynomials and general power functions using the power rule for integration.

Q1:

Determine ī„¸ī€š10đ‘Ĩ+21đ‘Ĩ−49ī…đ‘ĨīŠ¨d.

  • A10đ‘Ĩ+21đ‘Ĩ−49đ‘Ĩ+īŠŠīŠ¨C
  • B103đ‘Ĩ+212đ‘Ĩ−49đ‘Ĩ+īŠŠīŠ¨C
  • C5đ‘Ĩ+21đ‘Ĩ−49đ‘Ĩ+īŠŠīŠ¨C
  • D10đ‘Ĩ+C
  • E30đ‘Ĩ+42đ‘Ĩ−49đ‘Ĩ+īŠŠīŠ¨C

Q2:

Determine ī„¸ī€ŧ−4√đ‘Ĩ−5+7đ‘Ĩīˆđ‘ĨīŠ¨d.

  • A−4đ‘Ĩ+7đ‘Ĩ+īŠ¨C
  • B−8√đ‘Ĩ−7đ‘Ĩ+C
  • C−5đ‘Ĩ−8√đ‘Ĩ+7đ‘Ĩ+īŠŠC
  • D−5đ‘Ĩ−8√đ‘Ĩ3−7đ‘Ĩ+īŠŠC

Q3:

Determine ī„¸đ‘Ĩ−14đ‘Ĩđ‘Ĩ−14đ‘ĨīŠĒīŠŠd.

  • A3đ‘Ĩ+īŠĒC
  • B13đ‘Ĩ+īŠĒC
  • C14đ‘Ĩ+īŠĒC
  • Dđ‘Ĩ+īŠĒC
  • E4đ‘Ĩ+īŠĒC

Q4:

Determine ī„¸ī€ŧđ‘Ĩ−5đ‘Ĩīˆī€ŧđ‘Ĩ+5đ‘Ĩīˆī€ŧđ‘Ĩ+25đ‘Ĩīˆđ‘ĨīŠ¨īŠ¨d.

  • Ađ‘Ĩ4+6254đ‘Ĩ+īŠĢīŠŠC
  • Bđ‘Ĩ5−6253đ‘Ĩ+īŠĢīŠŠC
  • Cđ‘Ĩ3+125đ‘Ĩ+īŠŠīŠĢC
  • Dđ‘Ĩ5+6253đ‘Ĩ+īŠĢīŠŠC

Q5:

Determine ī„¸ī€ŧ3đ‘Ĩ−7đ‘Ĩīˆđ‘ĨīŠ¨d.

  • A13ī€ŧ3đ‘Ĩ−7đ‘Ĩīˆ+īŠŠC
  • B9đ‘Ĩ−42đ‘Ĩ+49đ‘Ĩ+īŠŠC
  • Cī€ŧ3đ‘Ĩ−7đ‘Ĩīˆ+īŠŠC
  • D3đ‘Ĩ−42đ‘Ĩ−49đ‘Ĩ+īŠŠC

Q6:

Determine ī„¸4đ‘Ĩ+đ‘Ĩ+12đ‘Ĩ+1đ‘ĨīŠŠd.

  • A2đ‘Ĩ3−đ‘Ĩ2+đ‘Ĩ+īŠŠīŠ¨C
  • B6đ‘Ĩ−2đ‘Ĩ+đ‘Ĩ+īŠŠīŠ¨C
  • C2đ‘Ĩ−đ‘Ĩ+đ‘Ĩ+īŠŠīŠ¨C
  • Dđ‘Ĩ−đ‘Ĩ+đ‘Ĩ+īŠŠīŠ¨C

Q7:

Determine ī„¸ī„Ÿī€ŧ8đ‘Ĩ−18đ‘Ĩīˆ+4đ‘ĨīŠ¨īŠ¨īŠ¨d.

  • A24đ‘Ĩ−18đ‘Ĩ+īŠŠīŠąīŠ§C
  • B8đ‘Ĩ−124đ‘Ĩ+īŠąīŠŠC
  • C8đ‘Ĩ+18đ‘Ĩ+īŠŠīŠąīŠ§C
  • D4đ‘Ĩ−116đ‘Ĩ+īŠŠīŠąīŠ§C
  • E83đ‘Ĩ−18đ‘Ĩ+īŠŠīŠąīŠ§C

Q8:

Determine ī„¸36đ‘Ĩ−49√đ‘Ĩ(6đ‘Ĩ+7)đ‘ĨīŠ¨īŽ§d.

  • A6đ‘Ĩ−7đ‘Ĩ+īŽ īŽ¤īŽ§īŽĻīŽ§C
  • B48đ‘Ĩ7+56đ‘Ĩ+īŽ īŽ¤īŽ§īŽĻīŽ§C
  • C16đ‘Ĩ5−8đ‘Ĩ+īŽ īŽ¤īŽ§īŽĻīŽ§C
  • D45đ‘Ĩ4−49đ‘Ĩ8+īŽ īŽ¤īŽ§īŽĻīŽ§C

Q9:

Determine ī„¸(4đ‘Ĩ+1)(2đ‘Ĩ−6)đ‘Ĩd.

  • A8đ‘Ĩ+C
  • B8đ‘Ĩ−22đ‘Ĩ−6đ‘Ĩ+īŠŠīŠ¨C
  • C4đ‘Ĩ−22đ‘Ĩ−6đ‘Ĩ+īŠŠīŠ¨C
  • D83đ‘Ĩ−11đ‘Ĩ−6đ‘Ĩ+īŠŠīŠ¨C
  • E24đ‘Ĩ−44đ‘Ĩ−6đ‘Ĩ+īŠŠīŠ¨C

Q10:

Determine ī„¸đ‘Ĩ−19đ‘Ĩ+70đ‘Ĩ−14đ‘ĨīŠ¨d.

  • A12ī€šđ‘Ĩ−19đ‘Ĩ+70ī…+īŠ¨īŠ¨C
  • Bđ‘Ĩ2−5đ‘Ĩ+īŠ¨C
  • Cđ‘Ĩ3−19đ‘Ĩ2+70đ‘Ĩ+īŠŠīŠ¨C
  • Dđ‘Ĩ2−14đ‘Ĩ+īŠ¨C

Q11:

Determine ī„¸(đ‘Ĩ+4)ī€šđ‘Ĩ−4đ‘Ĩ+16ī…đ‘ĨīŠ¨d.

  • Ađ‘Ĩ2+64đ‘Ĩ+īŠ¨C
  • B4đ‘Ĩ+64đ‘Ĩ+īŠĒC
  • Cđ‘Ĩ3+64đ‘Ĩ+īŠĒC
  • Dđ‘Ĩ4+64đ‘Ĩ+īŠĒC

Q12:

Determine ī„¸(đ‘Ĩ−6)(đ‘Ĩ−5)(đ‘Ĩ−3)đ‘Ĩd.

  • A18(đ‘Ĩ−6)(đ‘Ĩ−5)(đ‘Ĩ−3)+īŠ¨īŠ¨īŠ¨C
  • Bđ‘Ĩ−14đ‘Ĩ+63đ‘Ĩ−90+īŠŠīŠ¨C
  • Cđ‘Ĩ4−14đ‘Ĩ3+63đ‘Ĩ2−90đ‘Ĩ+īŠĒīŠŠīŠ¨C
  • Dđ‘Ĩ−14đ‘Ĩ+63đ‘Ĩ−90đ‘Ĩ+īŠĒīŠŠīŠ¨C

Q13:

Determine ī„¸âˆ’27đ‘Ĩđ‘ĨīŠąīŠ¯d.

  • A−27đ‘Ĩ+īŠąīŠŽC
  • B263đ‘Ĩ+īŠąīŠŽC
  • C128đ‘Ĩ+īŠąīŠŽC
  • D135đ‘Ĩ+īŠąīŠ§īŠĻC
  • E167đ‘Ĩ+īŠąīŠŽC

Q14:

Determine ī„¸âˆ’9đ‘Ĩ+79đ‘Ĩđ‘ĨīŠ¨īŠ¨d.

  • A−79đ‘Ĩ+C
  • B79đ‘Ĩ+C
  • C−đ‘Ĩ+79đ‘Ĩ+C
  • D−đ‘Ĩ−79đ‘Ĩ+īŠ¨C

Q15:

Determine ī„¸ī’(−9đ‘Ĩ+10)−8īžđ‘ĨīŠ¨d.

  • A−8đ‘Ĩ−18(−9đ‘Ĩ+10)+īŠ¨C.
  • B−24đ‘Ĩ−27(−9đ‘Ĩ+10)+īŠŠC.
  • C−8đ‘Ĩ+13(−9đ‘Ĩ+10)+īŠŠC.
  • D−8đ‘Ĩ−127(−9đ‘Ĩ+10)+īŠŠC.

Q16:

Determine ī„¸ī€ŧ8√đ‘Ĩ−1đ‘Ĩīˆđ‘ĨīŠĒd.

  • A8√đ‘Ĩ−1đ‘Ĩ+īŠŠīŠŠC
  • B16√đ‘Ĩ+14đ‘Ĩ+īŠŠīŠŠC
  • C163√đ‘Ĩ+13đ‘Ĩ+īŠŠīŠŠC
  • D12√đ‘Ĩ+3đ‘Ĩ+īŠŠīŠŠC
  • E−16√đ‘Ĩ+15đ‘Ĩ+īŠĢC

Q17:

Determine ī„¸7√đ‘Ĩđ‘ĨīŠŠd.

  • A7√đ‘Ĩ+īŠĢC
  • B145√đ‘Ĩ+īŠĢC
  • C143√đ‘Ĩ+īŠĢC
  • D70√đ‘Ĩ+īŠĢC
  • E14√đ‘Ĩ+C

Q18:

Determine ī„¸đ‘Ĩī€šđ‘Ĩ+2ī…đ‘ĨīŠ¨īŠ¨īŠ¨d.

  • Ađ‘Ĩ5+4đ‘Ĩ3+4đ‘Ĩ+īŠĢīŠŠC
  • B7đ‘Ĩ+20đ‘Ĩ+12đ‘Ĩ+īŠ­īŠĢīŠŠC
  • Cđ‘Ĩ6+đ‘Ĩ+2đ‘Ĩ+īŠ­īŠĢīŠŠC
  • Dđ‘Ĩ7+4đ‘Ĩ5+4đ‘Ĩ3+īŠ­īŠĢīŠŠC

Q19:

Determine ī„¸ī€ģ−4√đ‘Ĩ+8ī‡âˆšđ‘Ĩđ‘ĨīŽ¤īŽ¤īŠ¯īŠ¨d.

  • A−5đ‘Ĩ4+40đ‘Ĩ7+īŽ īŽĨīŽ¤īŽĻīŽ¤C
  • B−20đ‘Ĩ11+20đ‘Ĩ+īŽ īŽĨīŽ¤īŽĻīŽ¤C
  • C−64đ‘Ĩ5+56đ‘Ĩ5+īŽ īŽĨīŽ¤īŽĻīŽ¤C
  • D−72đ‘Ĩ73+16đ‘Ĩ7+īŽĻīŽĸīŽ īŽ§īŽĻīŽĄC

Q20:

Determine ī„¸ī€ŋ9√đ‘Ĩ+2đ‘Ĩ−1√đ‘Ĩī‹đ‘Ĩd.

  • A−√đ‘Ĩ+2đ‘Ĩ+9√đ‘Ĩ+īŠ¨īŠŠC
  • B12ī€ģ−2√đ‘Ĩ+đ‘Ĩ+6√đ‘Ĩī‡+īŠ¨īŠŠīŠ¨C
  • C−2√đ‘Ĩ+đ‘Ĩ+6√đ‘Ĩ+īŠ¨īŠŠC
  • D8√đ‘Ĩ+đ‘Ĩ+īŠ¨C

Q21:

Determine ī„¸ī€ģ3√đ‘Ĩ+1ī‡đ‘ĨīŽĸīŠ¨īŠ¨d.

  • A10đ‘Ĩ+36đ‘Ĩ+đ‘Ĩ+īŽ¤īŽĄīŠĒC
  • B12đ‘Ĩ5+9đ‘Ĩ4+đ‘Ĩ+īŽ¤īŽĄīŠĒC
  • C4đ‘Ĩ+3đ‘Ĩ+đ‘Ĩ+īŽ¤īŽĄīŠĒC
  • D27đ‘Ĩ7+18đ‘Ĩ5+đ‘Ĩ+īŽĻīŽĸīŽ¤īŽĸC

Q22:

Determine ī„¸8√đ‘Ĩđ‘ĨīŽ¤īŠŦd.

  • A−85đ‘Ĩ+īŠąīŽ īŽ¤C
  • B−203đ‘Ĩ+īŠąīŽ īŽ¤C
  • C−40đ‘Ĩ+īŠąīŽ īŽ¤C
  • D−4011đ‘Ĩ+īŠąīŽ īŽ īŽ¤C
  • E8đ‘Ĩ+īŠąīŽ īŽ¤C

Q23:

Determine ī„¸âˆšđ‘Ļ√đ‘Ļđ‘ĻīŽ¤īŽĸīŠ¨d.

  • A15đ‘Ļ16+īŽ īŽĨīŽ īŽ¤C
  • B16đ‘Ļ15+īŽ īŽĨīŽ īŽ¤C
  • C−1514đ‘Ļ+īŽ īŽŖīŽ īŽ¤C
  • D15đ‘Ļ+īŽ īŽĨīŽ īŽ¤C

Q24:

Determine ī„¸ī€šâˆ’7đ‘Ĩ−5ī…ī€šâˆ’đ‘Ĩ+1ī…đ‘ĨīŠ¨īŠŠd.

  • A7đ‘Ĩ4+5đ‘Ĩ2−7đ‘Ĩ+īŠĒīŠ¨C
  • B7đ‘Ĩ6+5đ‘Ĩ4−7đ‘Ĩ3−5đ‘Ĩ+īŠŦīŠĒīŠŠC
  • C7đ‘Ĩ5+5đ‘Ĩ3−7đ‘Ĩ2−5đ‘Ĩ+īŠŦīŠĒīŠŠC
  • D42đ‘Ĩ+20đ‘Ĩ−21đ‘Ĩ−5đ‘Ĩ+īŠŦīŠĒīŠŠC

Q25:

Determine ī„¸đ‘Ĩ+216đ‘Ĩ−6đ‘Ĩ+36đ‘ĨīŠŠīŠ¨d.

  • Ađ‘Ĩ3−3đ‘Ĩ+36đ‘Ĩ+īŠŠīŠ¨C
  • Bđ‘Ĩ2−6đ‘Ĩ+īŠ¨C
  • Cđ‘Ĩ4−216đ‘Ĩ+īŠĒC
  • Dđ‘Ĩ2+6đ‘Ĩ+īŠ¨C

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.