Integral of sqrt(x)/sqrt(1-x^3) (substitution)

Integral of sqrt(x)/sqrt(1-x^3) - How to integrate it step by step using the substitution method!

✅ 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞 𝐭𝐨 𝐜𝐡𝐞𝐜𝐤 𝐭𝐡𝐞 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧

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𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition

𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮

𝐃𝐨𝐧𝐚𝐭𝐞

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👋 Follow @integralsforyou for a daily integral 😉

𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition


𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
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[ernestschoenmakers]

A shortcut: sqrt(x)*dx = (2/3)*d(xsqrt(x)) and x^3 = (xsqrt(x))^2 so the integral becomes:
int of which is (2/3)*arcsin(xsqrt(x)) + C.

[gsg]

substitute x^3=sin^2(t), dx/dt=2cos(t)/3(sin(t))^1/3 ... works well

[syphaxjuba]

merci pour cette intégrale, excellent double changement de variable,

[gentlemandude]

Please periodically move your hand out of the way once you've written something down. For the majority of this video, the calculation can't be seen. It makes the process very hard to follow.

[monikaherath]

Your handwriting is absolutely wonderful!

[_jayjay]

substitute t = sqrt(1-x^3)

(-2/3) dt/x^2 = dx/sqrt(1-x^3)

sub back into integral
-2/3 integral x^(-3/2) dt

by manipulation, x^(-3/2) = 1/sqrt(1-t^2)

hence
(-2/3) integral [ 1/sqrt(1-t^2) ] dt

just apply rule on integral to obtain
-2/3 sin-1(t) + C

slightly longer but easier for me

[sleepystuff]

I am a new subscriber, in love with your channel.. where have you been all my life
Thank you so much 🙏

[jaspalverma]

pls solve a qstn for me
integral of (1-x^2)sinxcos^2x from pi to -pi

[diegoguerrero]

Podrías ayudarme por favor :)

Integral of dx/(x^2 sqrt(9 - x^2))
integrate 3x + 1 dx/x^2 + 4x + 3
integrate x dx/ x (x + 2)^2
integrate dx/ x^2 sqrt(4 + x^2)

[luisgianpierocastanedabarr]

Hola podrias ayudarme con esta integral?
Integral de dx/(x-3)sqrt(x^2-6x+5)

[satishdhage]

Please solve √x^2+1÷x^4 integration i.e. integration of under root x square +1 divided by x raised to 4

[darksaske]

Una pregunta: ¿por qué no se eliminan como primer paso ambas raíces de tanto numerador como denominador? ¿No simplificaría mucho más todo el proceso? En cualquier caso, gracias por el video, te has ganado un colacao!

[YOYO-zyyj]

Can we take root(1-x^3) as u and solve??

[chandrakumar]

Do me a favor. Please Integrate xarctanx/(1+x²)^(3/2) .
This has made me mad. No website has step by step solution for this😭😭

[gorangjangid]

do you get money from your videos ? asking coz i appreciate your work

[iguess]

Hi! Can you integrate (x^7/2)/sqrt(1-x^3). I can't find it anywhere :/

[culturalandeducational]

U =√x ->x^2=x->x^6=x^3 I can't understand please explain this..

[upender]

Hii.. I want the answer for integration of e^√x cose^√x/√x . Say the ans sir...

[NicolasSpiaggi]

I did u=x^(3/2) but I can't get the u^2 at the denominator to reach that arcsen formula. Google shows this way to solve it, but I don't know how to reach that f*** u^2. Hopefully you can see this and explain it to me. Also, I rewrote sqrts as exponents, you know, √x=x^(1/2)