Question

Find integral (x/(2x^2-3)^3)dx

Answer 1

\[\int\limits_{}^{}(x \div (2x ^{2}-3)^{3}) dx\]

Answer 2

whats the derivative of the bottom give us?

Answer 3

prolly a bad first thought by me tho

Answer 4

we can try to clean this up with a u sub

Answer 5

wait, what? okay lets do a u sub

Answer 6

the most likely candidate is to make u = 2x^2 - 3 so that we can just eat up that denominator

Answer 7

lets take the derivative of u now so that we can find a suitable replacement for dx

Answer 8

okay so with u=2x^2 - 3 the denominator is gone? okay lets find the derivative

Answer 9

not gone, but cleaned up so that we can better see it

Answer 10

oh okay i see what you mean

Answer 11

all that stuff is hidden inside or behind the u for now

Answer 12

u = 2x^2 - 3 we need to derive this for a suitabel dx replacement

u' = 4x x' ...

u'/4x = x'

du/4x = dx is fine

Answer 13

so lets start replacing stuff and simplifying

Answer 14

here it is

Answer 15

okay, would it be \[(-1\div4(2x ^{2}-3)^{4})+C\]

Answer 16

x x du
----------- dx ; ---- ---- = \(\large \frac{1}{4u^3}du\)
(2x^2-3) ^3 u^3 4x

Answer 17

@harishan16 we havent learned sec and tan yet

Answer 18

if you type in frac{a}{b} in the equation editor you get a prettier fraction

Answer 19

dx is not scaned in that img, but still u cant undstnd!

Answer 20

oh okay i was wondering how to do so

Answer 21

so this cleans up to:\[\frac{1}{4}\int u^{-3}du\]

Answer 22

by hiding everything we can behind us it cleans up nicely

Answer 23

so I send another easy method

Answer 24

my answer choices are \[\frac{-1}{2(2x ^{2}-3)^{2}} +C\] , \[\frac{-1}{4(2x ^{2}-3)^{4}}+C\] , \[\frac{-1}{16(2x ^{2}-3)^{4}}+C\]

Answer 25

you have to undo the u after you integrate

Answer 26

yeah @taffytwink when you sub out the u you'll end up with answer number 2

Answer 27

really?

Answer 28

or this answer \[\frac{-1}{8(2x ^{2}-3)^{2}}+C\]

Answer 29

that one looks better to me

Answer 30

my answer choices dont line up with your answer @harishan16

Answer 31

sorry, u hv to divide by two

Answer 32

if anything ^-3 ints up to ^-2/-2

Answer 33

so which of the four answer options do you think is right

Answer 34

integrate the u sub, finish it out and youll be able to pick it right out

Answer 35

how do i do that

Answer 36

um, the power rule for integration is the simplest thing id try ....

Answer 37

alright, the answer choice doesnt go that far though so im confused

Answer 38

-1/8(2x^2 -3)^2 +C

Answer 39

yes harishan has the correct answer

Answer 40

the real question apparently is why that would be the correct answer

Answer 41

i forgot how i figured it out but it was circled so i either calculated it or guessed it right

Answer 42

this is the corrected answer.

Answer 43

\[\frac{1}{4}\int u^{-3}du\]
is a rather basic integration and ints up with the power rule; afterwards you simply uncover the xparts behind the u

Answer 44

ohhh okay, thank you so much for explaining

Answer 45

heck yea @harishan16 thanks for all the help

Answer 46

good luck

Answer 47

@harishan16 you take out 1/4 not 1/2 :D the derivative of 2x^2 - 3 is 4xdx remember?

Answer 48

welcome

Answer 49

derivative of 2x^2 - 3 is 4xdx only if the derivative respect to x.
if that respect to x^2, that is 2.

Answer 50

ahh you took it wrt x^2 huh i see...i do wonder why the answer doesnt line up with the choices as well :/