Q: Does this integral look too hard? A: Yes but....

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  • ΠžΠΏΡƒΠ±Π»ΠΈΠΊΠΎΠ²Π°Π½ΠΎ: 1 ΠΎΠΊΡ‚ 2024
  • We will integrate x*e^sqrt(x^2+1) but how?
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ΠšΠΎΠΌΠΌΠ΅Π½Ρ‚Π°Ρ€ΠΈΠΈ • 12

  • @deathgam3rhdgt198
    @deathgam3rhdgt198 4 мСсяца Π½Π°Π·Π°Π΄ +17

    I was about to say the most diabolical thing when you boxed in the answer. Good thing you remember the +C at the end

  • @pawovado
    @pawovado 4 мСсяца Π½Π°Π·Π°Π΄ +10

    u^2=x^2+1 so 2udu = 2xdx so xdx = udu and then IbP

    • @stevenogbuehi3846
      @stevenogbuehi3846 4 мСсяца Π½Π°Π·Π°Π΄

      That's how I did too. Just use special substitution.

    • @pawovado
      @pawovado 4 мСсяца Π½Π°Π·Π°Π΄

      @@stevenogbuehi3846 i saw u = sqrt(x^2+1), you can also take u^2= x^2+1 and take the derivitive on both sides and Then integrate by party

    • @stevenogbuehi3846
      @stevenogbuehi3846 4 мСсяца Π½Π°Π·Π°Π΄

      Yes,that's what I saw as well.

  • @isobar5857
    @isobar5857 4 мСсяца Π½Π°Π·Π°Π΄ +6

    Could you not factorise the final answer to get a tidier solution? Or am I wrong?

    • @Ninja20704
      @Ninja20704 4 мСсяца Π½Π°Π·Π°Π΄ +3

      You could but it wouldn’t exactly be neater/tidier IMO.

    • @rogerkearns8094
      @rogerkearns8094 4 мСсяца Π½Π°Π·Π°Π΄ +2

      Yes, I agree; it would be neater without the awkwardly duplicated e-to-power term.

  • @cameronskellams5670
    @cameronskellams5670 4 мСсяца Π½Π°Π·Π°Π΄ +4

    e^(-x²) 😈😈😈

  • @yelr1136
    @yelr1136 4 мСсяца Π½Π°Π·Π°Π΄

    Can you go over the AP Calc BC FRQs?

  • @holyshit922
    @holyshit922 4 мСсяца Π½Π°Π·Π°Π΄

    It is easy to see suitable substitution and then integration by parts

  • @experimentbysaifanali7580
    @experimentbysaifanali7580 4 мСсяца Π½Π°Π·Π°Π΄

    Yes, 1st