Question

ran into an issue calculating... (calculus 2 single var)

Answer 1

\[\int4x(2x^2+3)^7dx\]\\[du=?\]

Answer 2

latex is wonky over here
\[\rightarrow u=2x^2+3\]\[\rightarrow du=?\]

Answer 3

@Nnesha sorry, I think I've confused myself again :(

Answer 4

I forgot my latex.

Answer 5

[\\\\fail_latex]////[]]

see ?

Answer 6

hardcore googling time ↑

Answer 7

ikr

Answer 8

good thing we can still view openstudy posts...

Answer 9

it poops out a huge brainly ad what you talkin bout

Answer 10

but I just close it ._.

Answer 11

mine has no X out sign though :c

Answer 12

rip

Answer 13

click out of the box ?

Answer 14

it will prob disappear ?

Answer 15

works for me

Answer 16

maybe it's my browser being lame lol
school computer.

help with math anyone?

Answer 17

\[\huge\rm u= \color{Red}{2x^2+3}\]\[\large\rm du= derivative~of~2x^2 + derivative ~of~3 \]

Answer 18

\[(2x^2+3)=2(2x)+0\]this?

Answer 19

correct
so \[\frac{du}{dx}=2(2x)+0\]

Answer 20

`du/dx` because we are taking the derivative of u with respect to x

Answer 21

wait, so adding "dx" is due to implicit differentiation or... ?

Answer 22

i can check your work. so whenever u finish post the work

Answer 23

dx is because we are taking the derivative with respect to x

Answer 24

so then \[du=u'dx\]this?

Answer 25

yes

Answer 26

okay I got it then :)
thank you!

Answer 27

okay \[dx=\frac{du}{4x}\]\[\int{4x(2x^2+3)^7}\rightarrow\int4x(u)^7\frac{du}{4x}\rightarrow\int{u^7du}\] @Nnesha I think I'm doing something wrong

Answer 28

*left out a \(dx\) in the first integral sorry

Answer 29

that's correct

Answer 30

now apply the power rule for anti derivative

Answer 31

\[\int u^7du\]\[\frac{u^8}{8}du\]I feel like this is wrong.

Answer 32

wait no I forgot + C at the end

Answer 33

yep so u^8/8 +C

Answer 34

oh so the \(du\) is because the differentiation wrt \(u\)?

Answer 35

du represent the derivative of u
anti derivative is backwards of Derivative
so basically you already have the derivative now you're integrating to
find the original function
in other words u^8/8+C is anti derivative in terms of u
replace u with `2x^2+3` to write it in terms of x

Answer 36

\[\frac{u^8}{8}+C\rightarrow\frac{(2x^2+3)^8}{8}+C\]

Answer 37

continue to simplify?

Answer 38

oops I have to go

Answer 39

no that's it!