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Integrate powers of x (indefinite integrals)

12th grade (Year 13 in England) · 16 questions · Common Core: HSF.BF.B.4 · England: A-level Pure Mathematics

Name

Date

Score/ 16

  1. Question 1

    Find ∫ 3x² dx. Leave out the + C.

    Answer

  2. Question 2

    Find ∫ (9x² + 2x + 8) dx. Leave out the + C.

    Answer

  3. Question 3

    Sam needs ∫ 3/x² dx. Which answer is correct?

    • A. −6/x³ + C
    • B. 3/x³ + C
    • C. 3·ln x + C
    • D. −3/x + C

  4. Question 4

    Find ∫ −4x dx. Leave out the + C.

    Answer

  5. Question 5

    Find ∫ (−6x² − 8) dx. Leave out the + C.

    Answer

  6. Question 6

    Kai needs ∫ 3/x² dx. Which answer is correct?

    • A. 3/x³ + C
    • B. −6/x³ + C
    • C. −3/x + C
    • D. 3/x + C

  7. Question 7

    Find ∫ 6x² dx. Leave out the + C.

    Answer

  8. Question 8

    Find ∫ (9x² − 2x + 8) dx. Leave out the + C.

    Answer

  9. Question 9

    Yuki needs ∫ 1/x² dx. Which answer is correct?

    • A. −1/x + C
    • B. 1/x³ + C
    • C. 1·ln x + C
    • D. 1/x + C

  10. Question 10

    Find ∫ −15x⁴ dx. Leave out the + C.

    Answer

  11. Question 11

    Find ∫ (−9x² + 8x − 3) dx. Leave out the + C.

    Answer

  12. Question 12

    Elena needs ∫ 4/x² dx. Which answer is correct?

    • A. 4/x + C
    • B. −8/x³ + C
    • C. 4/x³ + C
    • D. −4/x + C

  13. Question 13

    Find ∫ −8x³ dx. Leave out the + C.

    Answer

  14. Question 14

    Find ∫ (9x² + 8x − 6) dx. Leave out the + C.

    Answer

  15. Question 15

    Noah needs ∫ 12/x⁴ dx. Which answer is correct?

    • A. 12/x⁵ + C
    • B. 12·ln x + C
    • C. 4/x³ + C
    • D. −4/x³ + C

  16. Question 16

    Find ∫ 7x⁶ dx. Leave out the + C.

    Answer

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Answer key: Integrate powers of x (indefinite integrals)

  1. 1. 1*x^3

  2. 2. 3x^3+x^2+8x

  3. 3. D. −3/x + C

  4. 4. -2*x^2

  5. 5. -2x^3-8x

  6. 6. C. −3/x + C

  7. 7. 2*x^3

  8. 8. 3x^3-x^2+8x

  9. 9. A. −1/x + C

  10. 10. -3*x^5

  11. 11. -3x^3+4x^2-3x

  12. 12. D. −4/x + C

  13. 13. -2*x^4

  14. 14. 3x^3+4x^2-6x

  15. 15. D. −4/x³ + C

  16. 16. 1*x^7