Question

[\int\limits_{}^{}\frac{ e^{4/x} }{ x^{2} }]

please help :)

Answer 1

\[\int\limits_{}^{}\frac{ e^{4/x} }{ x^{2} }\]

Answer 2

let u = 4/x , what is dx?

Answer 3

4lnx?

Answer 4

no, derivative of: u = 4/x

Answer 5

i know 1/x is lnx

Answer 6

its not 4 ln x?

Answer 7

he isn't asking you to integrate 1/x

Answer 8

not integration

i am considering a u substitution, so we have to replace all the x parts appropriately

if we let u = 4/x, and take the derivative of u with respect to x, what do we get?

Answer 9

i understand, it's 4/x
wouldn't it be 4lnx

Answer 10

oh wow i was integrating

Answer 11

\[\frac{e^{4/x}}{x^2}dx\]
\[\frac{e^{u}}{x^2}dx\]
we need to replace the other x parts with u parts letting u = 4/x

Answer 12

latex seems to be on the fritx

Answer 13

**fritz

Answer 14

so it's deriv of 4x^-1 = -4x^-2

Answer 15

almost

du = -4x^(-2) dx

-du/4 = x^(-2) dx

Answer 16

ah i see now

Answer 17

e^u
---- du is our substitution
-4

Answer 18

now, this is a constant and a rather simple e^u run up

Answer 19

so (-1/4)(e^4/x)+c?

Answer 20

take the derivative to chk

Answer 21

http://www.wolframalpha.com/input/?i=derivative++-e%5E%284%2Fx%29%2F4

it works :)

Answer 22

deriv of (-1/4)(e^4/x)+C = (-1/4)(e^4/x)(4/x)'=(-1/4)(e^4/x)(-4/x^2)=(e^4/x)/x^2 woooo

Answer 23

lol wolfram makes me sad cause the step by step explanations helped me out a lot during cal I, but i'm too poor to pay for it right now lol :(

Answer 24

my next questions are trig integrations
i'm super super bad at these

Answer 25

\[\int\limits_{}^{}\frac{ (\tan^{-1}x)^{2} }{ 1+x^{2} }\]

Answer 26

is this like... replace 1+x^2 with cos or something?

Answer 27

what is the derivative of arctan(x)?

Answer 28

im sorry, had to verify email.

Answer 29

derivative of arctan = 1/1+x^2

Answer 30

do you see 1/(1+x^2) above?

Answer 31

\[\int\limits_{}^{}(\tan^{-1}(x))^2 \frac{1}{1+x^2}dx \]
so if you replace arctan(x) with u
then du=1/(1+x^2) dx

Answer 32

so what do you have?

Answer 33

(tan^-1x)^3/3?

Answer 34

+ c lol

Answer 35

ok cool