integral of x^3(e^x)

[@AlejandraRamirez-nb7kg]

muchas gracias, you had helped me a lot with my homework!

[@tomihq]

The tabular method help me a lot to understand how many times I should integrate
Thanks!

[@mathbyleo]

Cool.

[@mathbyleo]

Even faster and neater.

[@abigailmedeltoxtle9548]

I didn't know this method until now. It's so useful, thank you so much!!!!

[@gawthamipragathi4149]

Tabular method omg it's wonderful

[@cynthiaoe94]

I need to know how to do this: -5x^3e^x dx

[@r.santhosh4142]

Anna please integral la limit 0 to 1 apply panna answer Enna varum . answer mattum chat pannuga please please Anna .

[@mathbyleo]

Ok once we found the anti derivative we can plug in 1 for upper boundary minus zero plugged in for lower boundary. f(b)-f(a):{ 1^(3)*e^1}-{3*1^2*e^1}+{6*1e^1}-{6*e^1}+6=-2e+6 result

[@r.santhosh4142]

Thank you so much anna 🥰

[@chungleandthebims167]

i can't really tell what's an integral and what might be an open parentheses, seeing as I'm comparing the work I did to your process

[@mathbyleo]

you technically here apply the formula of IBP. and steps are: 1- decide which function is u ( which you need to make du by differentiating u) and 2- pick up dv ( which you will make up v by integrating dv) and plug into formula.

[@mathbyleo]

try to use big bracket that wraps outside carefully and inside seperately.

[@flames9508]

Tabular method needs to be nerfed

[@NyeinNyeinEI-y8k]

Thank you so much par sayar

[@tareqaziz6943]

thanks bro,,,,

[@sharonmabulay7566]

Can you help me how to integrate e^-5x x^2 dx where u= -5x

[@mathbyleo]

Step 1: apply change of variable. Let -5x=t
After that you will integrate and obtain : -1/125 * int ( e^t * t^2) dt
Step2: Now apply integration by parts formula
Let u= t^2 ( then du=2t dt) and dv= e^t ( then v is anti derivative of dv which is e^t )
Step3: now plug in everything into:
uv- int( v du) formula integrate and simply.

[@mathbyleo]

Without u sub directly apply integration by parts formula.
Let u=x^2 then du: 2x dx and let dv= e^-5x then v is the anti derivative : -1/5 * e^-5x the best use tabular method. You can check integration by part video I made that also shows practical method. If you check other IBP videos I made you will be fluent in these kind of integrals.

[@manisaishetty8326]

What if power of x is negative

[@mathbyleo]

Apply substitution first let t=-x
Then dt=-dx
Rewrite the integral in terms of t
Int(e^t*t^3 dt
Now start integration by parts :(uv-int ( v du)
Let u=t^3 and dv=e^t
Then du: 3t^2 and v=e^t

[@manisaishetty8326]

@@mathbyleo what we have to do if there is x^-3 in place of x^3

[@சின்னதுரைABC24F006]

X^2E^3dx=? What values

[@mathbyleo]

It is (e^3*x^3)/3 + C

[@mathbyleo]

e^3 is a constant so you technically integrating x^2 dx which is x^3/3

[@زينبالحوراءعليكاظمطعمه]

thanks 🌹🌹🌹

[@mathbyleo]

Thanks Zainab. :)

[@H2Ahub]

Thanks

[@mathbyleo]

You are welcome Hijfur.

[@fernandtt1282]

No entendí nada pero me ayudo ver como lo hiciste, genial!

[@mathbyleo]

Gracias por el bonito comentario. ¿Necesitas algún otro ejemplo paso a paso? se trata solo de la fórmula y el enchufe en sus valores u y dv primero, luego derivan u para obtener du e integran v para obtener v y enchufar en la fórmula: uv-integral of v du

[@fernandtt1282]

Muchas gracias! Me fue excelente en mi escuela gracias este video, pase al frente a explicarlo jaja

[@mathbyleo]

@@fernandtt1282 De nada. Me alegro de que te beneficies.

[@Minecraftcreater123]

Which language you talk to each other can you tell me

[@mathbyleo]

It is Spanish but I use translate. :)

[@kylezicari3860]

W vid

[@infectedfuture6685]

Thanks bro

[@mathbyleo]

You are very welcome.

[@r.santhosh4142]

Fast reply Anna please