Antiderivatives of Trigonometric Functions

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Questions and Answers

Qual es le antiderivative de ∫sinxdx?

cosx + c

Qual es le antiderivative de ∫cosxdx?

sinx + c

Qual es le antiderivative de ∫sec²xdx?

tanx + c

Qual es le antiderivative de ∫csc²xdx?

<p>cotx + c</p> Signup and view all the answers

Qual es le antiderivative de ∫secxtanxdx?

<p>secx + c</p> Signup and view all the answers

Qual es le antiderivative de ∫cscxcotxdx?

<p>-cscx + c</p> Signup and view all the answers

Qual es le antiderivative de ∫tanxdx?

<p>ln|secx| + c</p> Signup and view all the answers

Qual es le antiderivative de ∫cotxdx?

<p>ln|sin| + c</p> Signup and view all the answers

Qual es le antiderivative de ∫secxdx?

<p>ln|secx + tanx| + c</p> Signup and view all the answers

Qual es le antiderivative de ∫cscxdx?

<p>ln|cscx + cotx| + c</p> Signup and view all the answers

Qual es le antiderivative de ∫(1/x)dx?

<p>ln|x| + c</p> Signup and view all the answers

Qual es le antiderivative de ∫a^xdx?

<p>(a^x)/lna + c</p> Signup and view all the answers

Qual es le antiderivative de ∫lnxdx?

<p>xlnx - x + c</p> Signup and view all the answers

Qual es le antiderivative de ∫e^xdx?

<p>e^x + c</p> Signup and view all the answers

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Study Notes

Antiderivatives de Trigonometricas

  • ∫sinxdx resulta in cosx + c.
  • ∫cosxdx resulta in sinx + c.
  • ∫sec²xdx resulta in tanx + c.
  • ∫csc²xdx resulta in -cotx + c.
  • ∫secxtanxdx resulta in secx + c.
  • ∫cscxcotxdx resulta in -cscx + c.

Antiderivatives de Functions Logarithmicas e Exponential

  • ∫tanxdx resulta in ln|secx| + c.
  • ∫cotxdx resulta in ln|sinx| + c.
  • ∫secxdx resulta in ln|secx + tanx| + c.
  • ∫cscxdx resulta in ln|cscx + cotx| + c.
  • ∫(1/x)dx resulta in ln|x| + c.
  • ∫a^xdx resulta in (a^x)/lna + c.
  • ∫lnxdx resulta in xlnx - x + c.
  • ∫e^xdx resulta in e^x + c.

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