Question

How to integrate this?

Answer 1

INTEGRAATE WHAT ?

Answer 2

Integrate 4x^3e^x^4/4 dx.

Answer 3

\[\huge \int 4x^3e^{\frac{x^4}{4}}dx\]this?

Answer 4

If so... there's a u-substitution that's just begging to be used...

Answer 5

Yes, it is.

Answer 6

What you mean by u-substitution?

Answer 7

Let u = something in the integrand...

Answer 8

Okay, the x^3 or e^x^4/4?

Answer 9

Which do you think? :D
Pro-tip... usually, it's the bit involved with the 'more complicated' function.

sounds fuzzy, I know... so why not start with letting
\[\Large u = \frac{x^4}{4}\] and see where it goes? :)

Answer 10

So I need to differentiate or using others?

Answer 11

sure... what's du?

Answer 12

It will become x.right?

Answer 13

Nope... try again... (now is definitely not the time to forget how to differentiate D: )

Answer 14

du/dx=x^3.

Answer 15

That's right... or
\[\large du = x^3dx\]

Answer 16

\[\huge \int 4\color{red}{x^3}e^{\frac{x^4}{4}}\color{red}{dx}\]
This part is just du.

Answer 17

Okay,I got it.

Answer 18

\[\huge \int 4e^{\frac{x^4}{4}}\color{green}{du}\]

Answer 19

etc... okay, good, you got it :)

Answer 20

Just to finish it off...
\[\huge \int 4e^{\color{blue}u}\color{blue}{du}\]

Answer 21

So for the last I get 4e^u which is 4e^x^4/4. Is it correct?

Answer 22

Thanks terenzreignz. :)

Answer 23

That's right :)
(And it's TJ, btw)

Answer 24

Okay TJ. :D

Answer 25

hey, this is an indefinite integral, they might be expecting the +C at the end, just saying @Imtant ^_^

Answer 26

Okay, I notice that. Anyway, thanks again. :D