Question

In this question you are asked to determine (x^3)( e^((5x^4)+7)) dx by u substitution

Answer 1

Hint: let u = 5x^4 + 7

du/dx = 20x^3
du = 20x^3*dx
x^3*dx = du/20

Answer 2

Now enter the corresponding integral I in u resulting from your substitution. Your answer should depend only on u

Answer 3

I got what you sent but i dont understand the question I sent.

Answer 4

hopefully you see how `(x^3)( e^((5x^4)+7)) dx ` turns into `e^u*du/20` ?

Answer 5

yup

Answer 6

here is the real question

Answer 7

@jim_thompson5910 i think you understand more if you see the attachments i posted

Answer 8

ok let me think

Answer 9

thanks man

Answer 10

ok for 7.3, I think they just want the transformed integral before you actually do any integrating

so you'd have

\[\Large \int \frac{1}{20}e^u du\]

or

\[\Large \frac{1}{20}\int e^u du\]

Answer 11

alright , i will give it a shot

Answer 12

awesome got it right @jim_thompson5910 thanks

Answer 13

no problem

Answer 14

i am stuck on one more question, is it ok that you explain it to me? its in the attachment @jim_thompson5910

Answer 15

Try

\[\Large u = \log_{4}(x)\]

so,

\[\Large \frac{du}{dx} = \frac{1}{x*\ln(4)}\]
\[\Large \ln(4)*du = \frac{dx}{x}\]

Answer 16

hmm is that +7 inside the log argument? or no?

Answer 17

no it is not. its part of the function @jim_thompson5910

Answer 18

ok thanks

Answer 19

so
\[\Large \int \frac{(\log_4(x))^2-\sqrt{3}\log_4(x)+7}{x} dx\]
\[\Large \int \left((\log_4(x))^2-\sqrt{3}\log_4(x)+7\right)\frac{dx}{x}\]
\[\Large \int \left(u^2-\sqrt{3}u+7\right)*\ln(4)*du\]
\[\Large \ln(4)\int \left(u^2-\sqrt{3}u+7\right)du\]

the second 'u' is not under the square root

Answer 20

thanks, after that I would need to change the integrals to find the value correct ?@jim_thompson5910

Answer 21

you mean change the limits of integration?

Answer 22

yeah @jim_thompson5910

Answer 23

if x = 1, then

\[\Large u = \log_4(x) = \log_4(1) = ???\]

Answer 24

that equals 0.6021

Answer 25

no

Answer 26

type in `log(1)/log(4)` into your calculator

Answer 27

thats 0.25,

Answer 28

what calc do you have?

Answer 29

in attachment

Answer 30

ok hit the log key and hit 1

Answer 31

i get 0

Answer 32

yes so when you divide by log(4), whatever that is, the overall result of log(1)/log(4) will be 0

Answer 33

if x = 1, then

\[\Large u = \log_4(x) = \log_4(1) = 0\]

Answer 34

log(64)/log(4) = 3

so if x = 64, then

\[\Large u = \log_4(x) = \log_4(64) = 3\]

Answer 35

\[\large \int_{1}^{64} \frac{(\log_4(x))^2-\sqrt{3}\log_4(x)+7}{x} dx = \ln(4)\int_{0}^{3} \left(u^2-\sqrt{3}u+7\right)du\]
take note at how the limits of integration change

Answer 36

ahhh I see.

Answer 37

I will try and solve it from here now and i will send an image you to see if i got it right @jim_thompson5910

Answer 38

is this correct @jim_thompson5910 ?

Answer 39

how do they want you to enter the answer? as an exact number? or approximate decimal form?

Answer 40

i got it wrong but they gave me hints.

Answer 41

it would be nice if they posted the instructions on how to enter the answer. Hmm well if you're using an approximate value, then try 30.7837

that's what I'm getting as an approx value

Answer 42

i think they would like it in exact form. the system uses maple language

Answer 43

ah ok I see

Answer 44

in your work, I agree with lines 1 through 3. Line 4 is correct in terms of the right approx answer, but it's best to keep things exact as long as possible

so \(\Large \frac{\sqrt{3}(3)^2}{2}\) should turn into \(\Large \frac{9\sqrt{3}}{2}\)

Answer 45

thanks man for the help much! appreciated !! @jim_thompson5910