Understanding the Indefinite Integral
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Questions and Answers

What is the indefinite integral of $2x$ with respect to $x$?

  • $2x^2 + C$
  • $x^2$
  • $2x + C$
  • $x^2 + C$ (correct)
  • What is the indefinite integral of $4$ with respect to $x$?

  • $4 + C$
  • $4x + C$ (correct)
  • $4x^2 + C$
  • $4x$
  • What is the indefinite integral of $3x^2$ with respect to $x$?

  • $x^2 + C$
  • $x^3 + C$ (correct)
  • $3x^2 + C$
  • $3x^3 + C$
  • What is the indefinite integral of $5e^x$ with respect to $x$?

    <p>$5e^x + C$</p> Signup and view all the answers

    What is the indefinite integral of $7 ext{sin}(x)$ with respect to $x$?

    <p>$-7 ext{cos}(x) + C$</p> Signup and view all the answers

    What is the indefinite integral of $rac{1}{x}$ with respect to $x$?

    <p>$ ext{ln}|x| + C$</p> Signup and view all the answers

    What is the indefinite integral of $rac{1}{ ext{cos}^2(x)}$ with respect to $x$?

    <p>$ ext{tan}(x) + C$</p> Signup and view all the answers

    What is the indefinite integral of $rac{1}{1+x^2}$ with respect to $x$?

    <p>$ ext{arctan}(x) + C$</p> Signup and view all the answers

    What is the indefinite integral of $rac{1}{ ext{sin}(x) ext{cos}(x)}$ with respect to $x$?

    <p>$ ext{ln}| ext{tan}(x)| + C$</p> Signup and view all the answers

    What is the indefinite integral of $rac{x+1}{ ext{x}^2+2}$ with respect to $x$?

    <p>$rac{ ext{ln}|(x^2+2)|}{2}+ ext{x}+C$</p> Signup and view all the answers

    Study Notes

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    Test your understanding of the indefinite integral and its properties with this quiz. Questions cover techniques for finding indefinite integrals, substitution, integration by parts, and more.

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