Integral of 1/(16+x^2) (substitution)

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Integral of 1/(16+x^2) - How to integrate it step by step using the substitution method!

โœ… ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐ญ๐จ ๐œ๐ก๐ž๐œ๐ค ๐ญ๐ก๐ž ๐ฌ๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง

๐Ÿšถ ๐’๐ญ๐ž๐ฉ๐ฌ
00:00 Factor out 16
00:16 Take 1/16 outside the integral and rewrite x^2/16 as (x/4)^2
00:30 Substitution: u=x/4
00:37 Differentiate in both sides
00:47 Substitute x/4 and dx
01:08 Take 4 outside the integral
01:19 Simplify 4/16 and integrate 1/(1+u^2)
01:26 Undo substitution: u in terms of x
01:35 Add integration constant +C
01:42 Final answer!

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โ–บ Integration by parts

โ–บ Integration by substitution

โ–บ Integration by trig substitution

โ–บ Integration by Weierstrass substitution

โ–บ Integration by partial fraction decomposition

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๐Ÿ‘‹ Follow @integralsforyou for a daily integral ๐Ÿ˜‰

๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ญ๐ข๐จ๐ง ๐ฆ๐ž๐ญ๐ก๐จ๐๐ฌ ๐ฉ๐ฅ๐š๐ฒ๐ฅ๐ข๐ฌ๐ญ
โ–บ Integration by parts

โ–บ Integration by substitution

โ–บ Integration by trig substitution

โ–บ Integration by Weierstrass substitution

โ–บ Integration by partial fraction decomposition


๐…๐จ๐ฅ๐ฅ๐จ๐ฐ ๐ˆ๐ง๐ญ๐ž๐ ๐ซ๐š๐ฅ๐ฌ ๐…๐จ๐ซ๐˜๐จ๐ฎ
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IntegralsForYou
ะะฒั‚ะพั€

thank-you, I really appreciate channels like yours. It helps a lot.

zyggzag
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I was studying this subject when you notif came ๐Ÿ˜‚๐Ÿ‘ canโ€™t believe that

zbp
ะะฒั‚ะพั€

merci pour cette illustration et bonne continuitรฉ

syphaxjuba
ะะฒั‚ะพั€

Thank you for your video, why do we need to make the subsitution u=x/4? Isn't the integral of 1/(1+(x/4)^2) equal to arctan(x/4)?

milanaaa
ะะฒั‚ะพั€

Hello Sir, Can we use the formula 1/(x^2 + a^2) = 1/a (tan^-1(x/a))? since 'a' is 4 here?

abdulhafeezahmed
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just do the integral of 1/ax^2+bx+c . I did it in the past, I can help you if you struggle with the conditions or naything

oguzhantopaloglu
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I've been searching everywhere for help with an indefinite integral. x^2/sqrt(36-x^2) . Any tips on how to solve? thank you

seansanchez
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Please solve this integration of 1/โˆš5x^2 - 4

siddharth
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Hiii . firstt your channel helped me alot . I love to think fastly in math and become like you๐Ÿ˜…
Second can you please do the integral of (x+1)^2 / 2+x^2
And thank you in advance !!

nouralloush
ะะฒั‚ะพั€

Teacher plz teacher about integral1/(e^x - 9 e^(-x)) dx ๐Ÿ™

learntogether
ะะฒั‚ะพั€

Integration of (2x + 1)^2/x-2 with respect to x

siddharth
ะะฒั‚ะพั€

Is this problem the same as

Integral dx
=
16 + x^2

?

aur
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Teacher, i need problems integral of by parts.

PD: good vรญdeo

el_oso_grizzly_
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Sir difficult way can't understand๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ this question

shehzadshehzad