Question

help me to evaluate the following integrals;

Answer 1

yeah what is it

Answer 2

\[\int\limits_{}^{} \frac{ dx }{ (2x-7)^4 }\]

Answer 3

Set \[y=2x-7\]

Answer 4

u*

Answer 5

Just a quick u-sub is all it takes here :)

Answer 6

\[u=2x-7 \implies du = 2 dx\] should be a simple integration from there :)

Answer 7

please finish it up,i will see the process

Answer 8

Hey, maybe try setting it up yourself and I will tell you if you're on the right path or not!

Answer 9

im not using u-sub thats why i want to learn about it

Answer 10

i probably get -1/3(2x-7)^-3+c

Answer 11

Ah, well as the name says, we make a substitution, so since we've set \[u=2x-7\] we substitute this expression back into the integral and also since we are not integrating with respect to du, we would differentiate our u substitution as I have shown you above, so we get \[\int\limits \frac{ 1 }{ 2u^4 } du\]

Answer 12

\[\int\limits \frac{ 1 }{ (2x-7)^4 }dx \implies \int\limits \frac{ 1 }{ \color{red}{u}^4 } \color{red}{\frac{ du }{ 2 }}\] the red is the substitutions we made :)

Answer 13

where the 2 come from?

Answer 14

\[u=2x-7 \implies du = 2 dx \implies dx = \frac{ du }{ 2 }\]

Answer 15

Good?

Answer 16

du is always equal to 2dx?

Answer 17

No, because we are differentiating with respect to x, so here I think this should make it clear: \[u= 2x-7\]\[\frac{ du }{ dx } = 2 \implies \frac{ du }{ 2 } = dx\]

Answer 18

We do this because we are integrating respect to u now

Answer 19

i see..

Answer 20

yup i get it ^^ thanks

Answer 21

Great :)

Answer 22

can you help me to this much harder problem?

Answer 23

i will post another

Answer 24

I will try!