Integrating Exponential Functions - Examples 3 and 4

[mysstring1]

just like dy/dx=dy/du multiplied by du/dx. we are treating is as if they are algebraic fractions by cancelling out the du;s, but are we really doing that as algebra or it's just a way to simplify it ?

in ur example, you are treating du=2^x lnx dx as algebraic expressions by moving the lnx from RHS to left hand side(dividing both sides by lnx). how do you know that you should divide by lnx not sthg else? and how did you work out that derivative of 2^x equals to 2^xlnx?

[mysstring1]

how do we decide what to let U be equal to ? any tricks? coz each question differs largely , so how to determine what U is.

-when u found what u is, differentiating that you get du=expression. dx,then how do you work out what and how to rearrange this equation to give you what you want on the RHS?

[mysstring1]

for the first example, 1/ln2 ln[u]+c

why do we need absolute value sign for it and when do we include C>?thanku

[finalight]

hey, i got a problem on integrating this equation

(e^ax)* sin bx

mind integrating that for me? cause i'm stuck with the first part

[LukeNikolau]

The first example in this video I found to get even more and more confusing as you progressed through it... seemed a bit rushed. The absolute values threw me off quite a bit. The second example made a lot of sense though. Thank you for the video man.

[chiconium]

hi sir PATRICK... can u teach us on how to solve this equation.. {4^ln 1/X / x DX? plsss... bcoz ur a good in math.. :D

[benzyza666]

I have exams tmmrw T^T

[TheNumber2Pencil546]

after years of watching your videos, i just realized that we are both left handed!

[patrickJMT]

@TheNumber2Pencil546 hopefully you knew you were left handed prior to that ; )

[rave208]

wtf howd u get from deriving 2^x = 2^x. In 2

[arctcs]

@rave208 d (a^x) / dx = a^x * ln a. Its a differentiation rule

[Gazzawey]

@rave208 its a formula d/dx (a^x)=a^x.ln(a) a=R-(0)

[minakatani]

how did you get the absolute values?

[bhardwajankit42]

nice teaching sir!!

[SuperPowderkeg]

0 dislikes, i'm not surprised!! Thumb's up all the way!!!!

[patrickJMT]

@SuperPowderkeg ha, now someone will thumbs down just out of spite : )

[SuperPowderkeg]

@patrickJMT Never going to happen!!

[godspeed28]

@patrickJMT Especially because you made sure that comment is going to be stuck there at the very top. =P

[basketballby]

WHY CANT MY CALCULUS TEST PROBLEMS BE AS EASY AS YOUR EXAMPLES FML.

great video though. <3

[honorollko]

thank you :)



[honorollko]

why does the integration of 1/u = ln lul ???

[TheOptimusprime9]

@honorollko the answer is a really long proof. Instead of looking at all the complicated algebra I just treat the int 1/u = ln lul +c as an identity.

[jarjarannoya2]

@honorollko the derivative of ln x = 1/x

[InfiniteCemetary]

Your videos are very helpfull, thanks a ton!

[tanflash1314]

but not (2^x) . ln 2 dx

[tanflash1314]

Hello...

dU= (2^x) / ln 2 dx 

[NovaSage]

Great example!

[fazekaslaszlo]

2 excellent examples!!!

[ermitz90]

I wonder why it needs a modulus sign for that ln|2^x+1|...need help a bit..

[cupcakescent]

@ermitz90 I was wondering the same!

[eunkuk91]

great video it helped me alot

can you put up a video or a solution for e^((1+i)x) i cant seem to get the answer...

thnx

[Bob8199]

Awesome, calculus rules.

[oexnorth]

i always thought integration was a fun part of calculus. That and applications of partial derivitives in story problems. Maybe you should do one of those (rate of change of volume in a box at a given time, etc). Good vid as always.

[jjaausa]

hey patrickJMT do you use a camcorder or webcam and what model is it hope u dont mid

great vid I understand better now