Integral Calculus

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Trying to find ∫x*arctan(x)dx, but I can't figure out what do to after:

(1/2)x^2*arctan(x)-1/2∫x^2/(x^2+1) dx

  • Integral Calculus -

    In google type:

    wolfram alpha

    When you see list of results click on:

    Wolfram Alpha:Computational Knowledge Engine

    When page be open in rectangle type:

    integrate x*arctan(x)dx

    and click option =

    After few secons you will see result.

    Then click option : Show steps

  • Integral Calculus -

    great, I can find the steps and i have the answer already. i just don't understand the step to be made after (1/2)x^2*arctan(x)-1/2∫x^2/(x^2+1) dx

  • Integral Calculus -

    To solve that last integral, you have to use the substitution rule.

    u= x^2 + 1
    du= 2x

    Therefore the integral becomes:

    -1/2∫(2/u) du

    Factor out the 2

    -∫1/u du

    Integrate

    -ln(u)

    Which is equal to

    -ln(x^2 +1)

    Since u= x^2 + 1

  • Integral Calculus -

    I figured it out
    @Ethan, you can't substitute because it is x^2 over(x^2+1)

  • Integral Calculus -

    x^2/(x^2+1) = 1 - 1/(x^2+1)
    You can easily integrate that.

  • Integral Calculus -

    Sorry, I misread that as 2x instead of x^2.

  • Integral Calculus :) -

    No problem!

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