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Antiderivatives with the power rule worksheets Grade 12

Find indefinite integrals of polynomials with the power rule, adding + C.

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How to do it

Raise each power by 1 and divide by the new power. Add + C.

∫(−5x3−x2+3x+5) dx=−5x44−x33+3x22+5x+C\int (-5x^{3} - x^{2} + 3x + 5)\, dx = -\dfrac{5x^{4}}{4} - \dfrac{x^{3}}{3} + \dfrac{3x^{2}}{2} + 5x + C
raise each power by 1 and divide by the new power; add C\text{raise each power by }1\ \text{and divide by the new power; add }C∫xⁿ dx = xⁿ⁺¹ ÷ (n + 1) + C
−5x44−x33+3x22+5x+C-\dfrac{5x^{4}}{4} - \dfrac{x^{3}}{3} + \dfrac{3x^{2}}{2} + 5x + C

Example problems

  1. ∫(−4x+5) dx=\int (-4x + 5)\, dx =
  2. ∫(−4x−1) dx=\int (-4x - 1)\, dx =
  3. ∫(5x2−6x+3) dx=\int (5x^{2} - 6x + 3)\, dx =
  4. ∫(2x2+6x−7) dx=\int (2x^{2} + 6x - 7)\, dx =

Integrals

  1. Antiderivatives with the power rule
  2. Integrals of 1/x, eˣ, sin and cos
  3. Integration by u-substitution
  4. Evaluating definite integrals
  5. Area under a curve
  6. Area between two curves
  7. Average value of a function