Question

Integration using substitution......

Answer 1

\[\int\limits_{}^{}\left( e ^{x ^{1/3}} \right)dx/x ^{2/3}\]

Answer 2

\[\huge \int\limits e^{\frac{x}{2}} \frac{dx}{x^{\frac{2}{3}}} \]
?

Answer 3

ohhh mishi doing integration :P

Answer 4

Lol, watch me complete this :P

Answer 5

watch like a ""boss"" :P

Answer 6

Only if the person who asked this question responds..I don't want to do a wrong problem like last time wasoo :P

Answer 7

ok im here

Answer 8

Please confirm if the integral is right..

Answer 9

\[\int\limits_{}^{}e ^{x ^{1/3}dx}/x ^{2/3}\]

Answer 10

\[\huge \int\limits e^{\frac{x}{2}} \frac{dx}{x^{\frac{2}{3}}} \]?

Answer 11

\[\huge \int\limits\limits_{}^{}e ^{x ^{1/3}dx}/x ^{2/3}\]

Answer 12

yehh diya is correct i guess, mishoo get your glasses on :P

Answer 13

\[\huge \int\limits\frac{e^{\frac{1}{2}dx}}{x^{\frac{2}{3}}} \]
?

Answer 14

I am not blind.

Answer 15

set x^(1/3)= u
du = 1/3(x)^(2/3)dx
3(x)^(2/3)du = dx

thus we have that
\[3\int\limits_{}^{}e^{u}u^{2/3}du/u^{1/3}u^{1/3}\]
thus we have

3\[3\int\limits_{}^{}e^{u}du\]

Answer 16

this is mishooo with her glasses

Answer 17

im sorry i for some reason i dont see the translation

Answer 18

the answer is

3e^(x^(1/2)) + c

Answer 19

if you are getting a math processing error refresh your browser, if you dont see what I did then I can try to explain it in more depth

Answer 20

I made a mistake dammit

Answer 21

i almost got the same thing except instead of 1/2 i got 1/3?

Answer 22

set x^(1/3)= u
du = 1/3(x)^(2/3)dx
3(x)^(2/3)du = dx

thus we have that

\[3\int\limits_{}^{}x^{2/3}e^{u}du/x^{2/3}\]

Answer 23

the x^(2/3) crosses out and we end up with the answer I got

Answer 24

yeah it is suppose to be 1/3 sorry Its 5 in the morning and I have had 4 exams 12 hours spaced apart all week

Answer 25

3e^(x^(1/3)) + c
is the answer

Answer 26

thats ok australopithercus, its my last problem and i am having a hard time with these but thank so verymuch for your help

Answer 27

what are you having a hard time with?

Answer 28

do you understand my method?

Answer 29

i just get confused when getting the u and du

Answer 30

yes i do

Answer 31

Just remember that you are taking du/dx on both sides of the equation and we treat these notions like fractions so

du/dx = x^(1/3) du/dx
we take the derivative of x^(1/2) it is
du/dx = 1/3(x)^(2/3)
multiply both sides by dx
we get
du = 1/3(x)^(2/3)dx
since we are performing substitution we need to solve for dx
thus we get
du(3(x)^(2/3)) = dx

now we can just replace dx with du

Answer 32

I hope this helps explain the process, and makes it a little less confusing

Answer 33

thank you