Question

the indefinite integral i am given is (e^x - 6x^2)/6... i need to evaluate it. please help!

Answer 1

Do you know the integral of e^x and the power rule?

Answer 2

i assume the integral is e^x

Answer 3

i need to use substitution, but i dont know what to substitute... i've tried it a lot already

Answer 4

You don't need to use any elevated integration techniques. If you want to prove that your result is right, just differentiate it and if you get the original integrand, you're fine.

Answer 5

what about the 6 in the denominator? how do i do that?
is it just 6x?

Answer 6

No, that is just a factor of 1/6 which you can pull-out.

Answer 7

wow.. i got it! thanks! i have another one tho if u are willing to help?

Answer 8

Sure :-)

Answer 9

(5-2xe^x)/x

Answer 10

Pull that division into the difference and you should have two known integrals.

Answer 11

like (5/x)-((2xe^x)/x)?

Answer 12

Yes, and reduce that x in the second term.

Answer 13

ok. then i would need substitution right?

Answer 14

For what? You should know the integral of 1/x and e^x and that's all there is.

Answer 15

i dont know the 1/x one. is it natural log?

Answer 16

Exactly, sometimes it is defined this way \[\ln x := \int_1^x\frac 1 y \mathrm d y\] but if you have defined it as the inverse function of e^x you could use the inverse-differentiation rule.

Answer 17

i got that one! thanks a lot. this is my last one... (x-2)/(x^2-4x+4)^3..... that requires substitution correct?

Answer 18

Yes, a little one :-) but you should first observe that \[x^2 - 4x + 4 = (x-2)^2\]

Answer 19

so i can cancel one of them right away?

Answer 20

yes

Answer 21

would it turn into (x-2)^6?

Answer 22

in the denominator

Answer 23

Sure, that is just one of the exponentiation rules.

Answer 24

then after the cancellation i am left with 1/(x-2)^5?

Answer 25

Right.

Answer 26

now i substitute u=x-2

Answer 27

Yes, but as du/dx = 1 if you are a little more experienced you could just do it in your head.

Answer 28

i think it would be 1/((1/6)*(x-2)^6)

Answer 29

Not quite, maybe you should write it is \[(x-2)^{-5}\] instead to see it better.

Answer 30

(-1/4)*(x-2)^-4?

Answer 31

Yeah, good.

Answer 32

is this website free to use?

Answer 33

It costs both of us our time, but you won't have to pay for it ;-)

Answer 34

so y do ppl like u go around and answer questions?

Answer 35

I love math and helping other people.

Answer 36

it seems strange that there is no charge for this service. or breech of security

Answer 37

I don't know what you mean by breech of security; but the idea of being is just that everyone can ask questions and give answers here. So if I had a question regarding my study, I could ask them too. Only that it seems there are a lot of high-school students here lately :-D

Answer 38

hmm... thats cool. i guess i'm a skeptic. but with quick responses like the ones u gave me i am becoming a believer