1. ## Integrales

Hello Guys,

I don't know how to solve this:

t/ (racine) 1 + t^2 ==> for this i did this: ?

Thanks

2. are you not fimmilar with inegrals in the form of $\displaystyle \int f(x)f'(x) dx$ ?

use should know and be able to easily prove that $\displaystyle \int f(x)f'(x) dx= \frac{1}{2} (f(x))^2$

Can you apply this to your integral ?

3. Originally Posted by bobak
are you not fimmilar with inegrals in the form of $\displaystyle \int f(x)f'(x) dx$ ?

use should know and be able to easily prove that $\displaystyle \int f(x)f'(x) dx= \frac{1}{2} (f(x))^2$

Can you apply this to your integral ?
ah so , Lnx/x = 1/2 Lnx?

4. Originally Posted by iceman1
ah so , Lnx/x = 1/2 Lnx?
please be careful with your notation, what you wrote makes no sense.

I am sure you meant to write.

$\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C$

5. Originally Posted by bobak
please be careful with your notation, what you wrote makes no sense.

I am sure you meant to write.

$\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C$
Yeah sorry but i don't know how to write a mathematics letters

so

==> this (integrale) 1/2 Ln (x)^2
==> 1/2 [Ln(1)^1 -Ln(x)^e)]
right?

6. you did not substitute the limits in the correct order. and you also confused
$\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C$ for $\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^x + C$

also you should know that $\displaystyle \ln 1 = 0$ and $\displaystyle \ln e = 1$

7. Originally Posted by bobak
you did not substitute the limits in the correct order. and you also confused
$\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C$ for $\displaystyle \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^x + C$

also you should know that $\displaystyle \ln 1 = 0$ and $\displaystyle \ln e = 1$
yay so the final results is 1/2 right?

what abt the other one?
i move it and change the puissance signe like this:
with integral from sure

8. yeah the answer is 1/2.

for the next one you should recognise that you have something in the form of

$\displaystyle \int kf'(x)[f(x)]^n dx = k \frac {[f(x)]^{n+1}}{n+1}$ can you finish it off ?

9. Originally Posted by bobak

for the next one you should recognise that you have something in the form of

$\displaystyle \int kf'(x)[f(x)]^n dx = k \frac {[f(x)]^{n+1}}{n+1}$ can you finish it off ?
ok i'll try:
2[t (1 + t^2)]^+1/2 divided by (1/2) (with integrales)

right?

10. almost check you got the value of the constant correct and differentiate to result to check your answer.

11. Using many formulae for these problems, it's an incredibly bad idea.

These are routine problems, so we don't need formulae to make this work.

Originally Posted by iceman1
Substitute $\displaystyle u^2=1+t^2.$

(Correct english forms for $\displaystyle \sqrt{~~}$ and $\displaystyle \int$ are square root and integral.)

12. Originally Posted by Krizalid
Using many formulae for these problems, it's an incredibly bad idea.

it not about using a formula, it more about identifying a standard form.

13. ok Thanks Guys

i have another thing:

f(x)= e^(-x) (+x) -1

Limit(+infinity)e^(-x) (+x) -1 = + infinity
Limit(-infinity)e^(-x) (+x) -1 = + infinity

right?