Sorry it has been awhile for me.

1. Do you guys know how to integrate

y(x) = 2x / (x^2 + 3) ???

2. The integral of e^(x^2) is 1/(2x)*e^(x^2) correct?

Thanks

i would probably know how to do that, had i not dropped my current calculus class. so the best i can do is say check for yourself!!!!!!


http://integrals.wolfram.com/


the integrator .. works nice

<i>1. Do you guys know how to integrate

y(x) = 2x / (x^2 + 3) ???</i>

Yes.

Put u = x^2 + 3
Then du/dx = 2x

Integral (2x / (x^2 +3)) dx
= Integral ((du/dx) / u) dx
= Integral (1/u) du
= ln u + c
= ln (x^2 + 3) + c

<i>2. The integral of e^(x^2) is 1/(2x)*e^(x^2) correct?</i>

No. You can see that's wrong by differentiating your answer.

mathematica says the answer is Log(3+x^2)

Log in mathematica is ln i believe, from the version i used at school

On Radioactive Waves,

Indeed it is, mostly log = ln, and log10 equals just what it says (the inverse function of powers of ten). Some books/courses prefer the distinct notation log for log10 and ln for the inverse of the exponential.

The lesson is: always check the convention used in a text before reading the formula's. Something which goes far beyond ln/log confusion :)

Bye!

Crisp

I advise you to buy Micheal Kelley's Mastering the AP Calculus AB + BC by ARCO

It's the best calculus prep book out there. It'll help you to understand everything - limits, integrals, differentiation, to slope/field solutions graphs.

man i used to be good at this
now im just lazy
:rolleyes:

Q2. im pretty sure thats wrong. I always just used to work backwards if i wasnt sure.

Good Luck

Hm. I thought the denominator would be an arctan when you integrated it...I dunno. I took calculus and I ended up with an A but I'm a slacker. I'll try to work it out.

If the arctan is wrong you might try substitution.

From memory, the integral of e^(x²) is related to the gamma function.