Table of Antiderivatives

Antiderivatives (indefinite integrals) of the most common functions: powers, 1/x, 1/√x, sine, cosine, eˣ and other exponentials, 1/cos²x and 1/sin²x. Don't forget the constant C.

10 formulas · Grade 11

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All 10 formulas on this page
  1. Antiderivative of a power function
  2. Antiderivative of a constant
  3. Antiderivative of 1/x
  4. Antiderivative of 1/√x
  5. Antiderivative of sine
  6. Antiderivative of cosine
  7. Antiderivative of 1/cos²x
  8. Antiderivative of 1/sin²x
  9. Antiderivative of an exponential function
  10. Antiderivative of eˣ

Antiderivative of a power function

Grade 11
F(x)=xn+1n+1F(x) = \frac{x^{n+1}}{n+1}

Antiderivative of the power function xⁿ for n ≠ −1.

Legend:
  • x — Value x
  • n — Exponent n

Antiderivative of a constant

Grade 11
F(x)=kx+CF(x) = kx + C

Antiderivative of a constant k.

Legend:
  • k — Coefficient k
  • x — Value x

Antiderivative of 1/x

Grade 11
F(x)=ln⁡∣x∣+CF(x) = \ln|x| + C

Antiderivative of the inverse-proportionality function.

Legend:
  • x — Value x

Antiderivative of 1/√x

Grade 11
F(x)=2x+CF(x) = 2\sqrt{x} + C

Antiderivative of the reciprocal of the square root of x.

Legend:
  • x — Value x

Antiderivative of sine

Grade 11
F(x)=−cos⁡x+CF(x) = -\cos x + C

Antiderivative of the sine function.

Legend:
  • deg — Angle x (in degrees)

Antiderivative of cosine

Grade 11
F(x)=sin⁡x+CF(x) = \sin x + C

Antiderivative of the cosine function.

Legend:
  • deg — Angle x (in degrees)

Antiderivative of 1/cos²x

Grade 11
F(x)=tg⁡x+CF(x) = \operatorname{tg} x + C

Antiderivative of the reciprocal of cosine squared.

Legend:
  • deg — Angle x (in degrees)

Antiderivative of 1/sin²x

Grade 11
F(x)=−ctg⁡x+CF(x) = -\operatorname{ctg} x + C

Antiderivative of the reciprocal of sine squared.

Legend:
  • deg — Angle x (in degrees)

Antiderivative of an exponential function

Grade 11
F(x)=axln⁡a+CF(x) = \frac{a^x}{\ln a} + C

Antiderivative of an exponential function with an arbitrary base a.

Legend:
  • a — Base a (a>0, a≠1)
  • x — Value x

Antiderivative of eˣ

Grade 11
F(x)=ex+CF(x) = e^x + C

Antiderivative of the exponential function eˣ.

Legend:
  • x — Value x

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