Antiderivative Rules Flashcards
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Questions and Answers

Qual es le resultato de ∫K dx?

Kx + C

Qual es le resultato de ∫0 dx?

C

Qual es le resultato de ∫xⁿ dx?

(xⁿ⁺¹)/(n+1) + C

Qual es le resultato de ∫(1/x) dx?

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

Qual es le resultato de ∫e^x dx?

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

Qual es le resultato de ∫e^ax dx?

<p>(e^ax)/a + C</p> Signup and view all the answers

Qual es le resultato de ∫a^x dx?

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

Qual es le resultato de ∫a^xlna dx?

<p>a^x + C</p> Signup and view all the answers

Qual es le resultato de ∫cosx dx?

<p>sinx + C</p> Signup and view all the answers

Qual es le resultato de ∫sinx dx?

<p>-cosx + C</p> Signup and view all the answers

Qual es le resultato de ∫sec²x dx?

<p>tanx + C</p> Signup and view all the answers

Qual es le resultato de ∫secxtanx dx?

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

Qual es le resultato de ∫csc²x dx?

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

Qual es le resultato de ∫cscxcotx dx?

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

Qual es le resultato de ∫tanx dx?

<p>-ln |cosx| + C</p> Signup and view all the answers

Qual es le resultato de ∫1/(x² + 1) dx?

<p>arctanx + C</p> Signup and view all the answers

Qual es le resultato de ∫1/(√(1-x²)) dx?

<p>arcsinx + C</p> Signup and view all the answers

Study Notes

Regulas de Antiderivadas

  • ∫K dx equale a Kx + C, ubi K es un constante.
  • ∫0 dx resulta in C, representando un constante d' integrazione.
  • ∫xⁿ dx se calcula como (xⁿ⁺¹)/(n+1) + C, valid pro n ≠ -1.
  • ∫(1/x) dx da ln |x| + C, unus forma typic de loja logarithmica.
  • ∫e^x dx produce e^x + C, mostra que la funzione exponentiale es su propia derivada.
  • ∫e^ax dx resulta in (e^ax)/a + C, ubi 'a' es un constante scalar.
  • ∫a^x dx equale a (a^x)/ln a + C, adonde 'a' es un base positiva.
  • ∫a^x ln a dx resulta in a^x + C, representando la relación entre logarithmo e exponentes.
  • ∫cosx dx da sinx + C, hilante le function cosine e sine.
  • ∫sinx dx produce -cosx + C, mostrando que la derivada de cosine es negativa.
  • ∫sec²x dx da tanx + C, connecente funciones secante e tangent.
  • ∫secxtanx dx resulta in secx + C, vincula secante e tangent in derivadas.
  • ∫csc²x dx equale a -cotx + C, donde csc es le cosecante.
  • ∫cscxcotx dx produce -cscx + C, interconectando csc e cot en problema de integrazione.
  • ∫tanx dx resulta in -ln |cosx| + C, adestra la function tangent con logarithmi.
  • ∫1/(x² + 1) dx da arctanx + C, cortando un legame profunde entre funciones trigonometric e algebraic.
  • ∫1/(√(1-x²)) dx produce arcsinx + C, mostrando la relazione di derivate con la circonferentia.

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Explore essential antiderivative rules with this set of flashcards. Each card provides a rule and its corresponding formula, aiding in understanding and retention. Perfect for students at various levels of calculus.

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