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Integrals of 1/x, eˣ, sin and cos worksheets Grade 12

Find antiderivatives of 1/x, eˣ, sin x and cos x.

The front of the free integrals of 1/x, eˣ, sin and cos worksheet
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Free · Worked example · 30 problems · Answer key · US Letter

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How to do it

∫(1 ÷ x) dx = ln|x| + C, ∫eˣ dx = eˣ + C, ∫cos x dx = sin x + C, ∫sin x dx = −cos x + C.

∫4ex dx=4ex+C\int 4e^{x}\, dx = 4e^{x} + C
ex is its own antiderivativee^{x}\ \text{is its own antiderivative}
4ex+C4e^{x} + C

Example problems

  1. ∫7x dx=\int \dfrac{7}{x}\, dx =
  2. ∫3x dx=\int 3\sqrt{x}\, dx =
  3. ∫6 cos⁡x dx=\int 6\ \cos x\, dx =
  4. ∫8 sin⁡x dx=\int 8\ \sin x\, 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