Question

Antidifferentiation help needed!

Answer 1

1. I don't get the concept behind finding the integral of 5x(1+ x^(2))^4
2. Also 2xe^(x)^(2)
3. How do you find the integral of sqrt(e^(x))?

Answer 2

I need step by step for 3.

Answer 3

All these are u-substitution problems

Answer 4

how?

Answer 5

if you understand how to work out one problems, others will be easy

Answer 6

okay

Answer 7

lets start with first problem

Answer 8

\(\large \int 5x(1+ x^2)^4 dx\)

Answer 9

substitute the stuff inside parenthesis as "u" :

\(\large u = 1+x^2\)

Answer 10

thats step 1

Answer 11

step 2 : find out "dx" in terms of "du" :


\(\large u = 1+x^2\)

differentiate both sides

\(\large du = 2x dx\)

\(\large \frac{du}{2} = x dx\)

Answer 12

substitute these in the integral :

\(\large \int 5x(1+ x^2)^4 dx\)

becomes :

\(\large \int 5(u)^4 \frac{du}{2}\)

Answer 13

fine, so far ?

Answer 14

?

Answer 15

? for which step ?

Answer 16

yes

Answer 17

no i get it now

Answer 18

what about step 3?

Answer 19

how do u knw there are 3 steps ? :)

Answer 20

last step is to evaluate the integral and substitute back ur x

Answer 21

y = sqrt(e^x)

y^2 = e^x

y^3/3 = e^x + C

i wonder if this is appropriate :)

Answer 22

its not lol

Answer 23

integral sign is missing lol

Answer 24

y = \int sqrt(e^x) dx

Answer 25

?

Answer 26

you wanto do the 3rd problem @AnImEfReaK ?

Answer 27

i don't get it still

Answer 28

which one ?
you're still doing first problem ?

Answer 29

yes is there a simpler method? i'm not familiar with du on its own. I have never done it that way or our class :/

Answer 30

what way you're doing in ur class ?
can u show an example problem ?

Answer 31

mhm, lol i use to think u-substitution is an universal method

Answer 32

ok

Answer 33

wait a moment

Answer 34

take ur time !

Answer 35

I am intrigued :3