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anonymous

  • one year ago

How to prove the indefinite integral of arctanx?

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  1. freckles
    • one year ago
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    the question seems incomplete do you want to prove it is an even function? is the question not to prove it and just find it?

  2. freckles
    • one year ago
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    what do you want to prove about it exactly?

  3. anonymous
    • one year ago
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    I just want to prove its solution

  4. anonymous
    • one year ago
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    http://math.stackexchange.com/questions/629940/a-definite-integral-containing-arctan-x Don't know if this site will help you @freckles

  5. freckles
    • one year ago
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    you mean find it solution? because this question is incomplete

  6. freckles
    • one year ago
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    find its solution*

  7. anonymous
    • one year ago
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    \[\int\limits_{}^{}arctanx\]

  8. anonymous
    • one year ago
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    yeah the solution'

  9. anonymous
    • one year ago
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    not a proof i guess then

  10. freckles
    • one year ago
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    oh ok because this question reminds me of saying something like prove 5 like prove 5 is what :p

  11. freckles
    • one year ago
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    anyways you could do a substituion let u=arctan(x) then tan(u)=x differentiating both sides gives sec^2(u) du=dx

  12. freckles
    • one year ago
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    \[\int\limits_{}^{} u \sec^2(u) du\]

  13. freckles
    • one year ago
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    try integration by parts

  14. freckles
    • one year ago
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    you could actually do integration by parts even before substitution

  15. anonymous
    • one year ago
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    so u=arctanx and dv=dx?

  16. freckles
    • one year ago
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    yeah

  17. anonymous
    • one year ago
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    i got xarctanx - 1/2ln(1+x^2)

  18. anonymous
    • one year ago
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    +C

  19. freckles
    • one year ago
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    \[\int\limits_{}^{} 1 \cdot \arctan(x) dx \\ =x \arctan(x)-\int\limits x \frac{1}{1+x^2} dx\] and yes for the second integral you are right because you can just do the sub u=1+x^2

  20. anonymous
    • one year ago
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    ok thank you! was a lot simpler than i realized

  21. freckles
    • one year ago
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    and @A.S.L. my question was not about integrating arctan(x) it was about what the prove meant before that part...

  22. freckles
    • one year ago
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    for example "evaluate the indefinite integral of arctan(x)" I would have no questions about this meaning

  23. anonymous
    • one year ago
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    Sorry My mistake @freckles

  24. freckles
    • one year ago
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    no apologies necessary

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