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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

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  1. Question 1

    Find ∫ (−9x² − 6x + 5) dx. Leave out the + C.

    Answer

  2. Question 2

    Sofia needs ∫ 6/x³ dx. Which answer is correct?

    • A. 6/x⁴ + C
    • B. −3/x² + C
    • C. −18/x⁴ + C
    • D. 6·ln x + C

  3. Question 3

    Find ∫ −12x³ dx. Leave out the + C.

    Answer

  4. Question 4

    Find ∫ (−3x² + 2x + 5) dx. Leave out the + C.

    Answer

  5. Question 5

    Yuki needs ∫ 9/x⁴ dx. Which answer is correct?

    • A. 3/x³ + C
    • B. 9·ln x + C
    • C. 9/x⁵ + C
    • D. −3/x³ + C

  6. Question 6

    Find ∫ 8x dx. Leave out the + C.

    Answer

  7. Question 7

    Find ∫ (6x² − 2x − 1) dx. Leave out the + C.

    Answer

  8. Question 8

    Mateo needs ∫ 3/x⁴ dx. Which answer is correct?

    • A. −1/x³ + C
    • B. 3/x⁵ + C
    • C. −12/x⁵ + C
    • D. 3·ln x + C

  9. Question 9

    Find ∫ 35x⁶ dx. Leave out the + C.

    Answer

  10. Question 10

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

    Answer

  11. Question 11

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

    • A. 1/x + C
    • B. −2/x³ + C
    • C. 1/x³ + C
    • D. −1/x + C

  12. Question 12

    Find ∫ 6x² dx. Leave out the + C.

    Answer

  13. Question 13

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

    Answer

  14. Question 14

    Luis needs ∫ 2/x³ dx. Which answer is correct?

    • A. 2/x⁴ + C
    • B. 2·ln x + C
    • C. 1/x² + C
    • D. −1/x² + C

  15. Question 15

    Find ∫ 24x⁵ dx. Leave out the + C.

    Answer

  16. Question 16

    Find ∫ (−3x² − 6x − 6) dx. Leave out the + C.

    Answer

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  1. -3x^3-3x^2+5x
  2. −3/x² + C
  3. -3*x^4
  4. -x^3+x^2+5x
  5. −3/x³ + C
  6. 4*x^2
  7. 2x^3-x^2-x
  8. −1/x³ + C
  9. 5*x^7
  10. 2x^3-8x
  11. −1/x + C
  12. 2*x^3
  13. x^3-4x^2-9x
  14. −1/x² + C
  15. 4*x^6
  16. -x^3-3x^2-6x