Antiderivative problem [$10 Reward]
 

Okay thanks for trying to help me. I am writing an important school test tomorrow and I still have a question which nobody could answer me.

I am looking for the antiderivative (no clue if thats the right word - if you have no idea what I am talking about tell me and I will try to find the right word in English!) of a formula such as this one:

1000
------
1+3x


or

1000x
-------
x²+16

Can you give me the answers and a way to get there?!?!?

I asked 2 friends of mine who are studying math at college and they couldn't help me (one had an answer but couldn't tell me how he got there)! I think this shouldn't be too hard for experts like you so it would be great if you could help!

Re: Antiderivative problem
 

Allright I am in a hurry so I will give the first one to post the right answer with an good explanation (which I can understand) $10 onto your Stars Account !!!
I won't say I didn't get it afterwards even if I did. You can trust me but right now I just feel helpless! Please take a minute to solve and explain (even a good Link would be great) this to me. Thanks!

Re: Antiderivative problem
 

You mean

1000x
-------
x^2 + 16

for the last one.

Hint: d/dx (ln u) = (du/dx)/u

Re: Antiderivative problem
 

[ QUOTE ]

Hint: d/dx (ln u) = (du/dx)/u

[/ QUOTE ]

If you could explain and/or just plug the numbers in and show how you get an answer the money is on it's way.

Re: Antiderivative problem
 

d/dx(ln(ax+b)) = a/(ax+b)

so d/dx(1000/3 ln(3x+1)) = 1000/(3x+1)

Re: Antiderivative problem
 

[ QUOTE ]
[ QUOTE ]

Hint: d/dx (ln u) = (du/dx)/u

[/ QUOTE ]

If you could explain and/or just plug the numbers in and show how you get an answer the money is on it's way.

[/ QUOTE ]

1) You know how to take the antiderivative of the left side of this equation.

2) Can you find a choice of u such that your functions look like C * (du / dx) / u, where C is some constant?

Re: Antiderivative problem
 

Yes! Thanks so much!
Just tell me your PS Acc (PM would be best)!!!

Re: Antiderivative problem
 

int[1000x/(x^2+16)]dx is ln(x^2+16)*500

Now we check that the derivative of ln(x^2+16)*500 =1000x/(x^2+16)

Since we know that the derivative of lnx =1/x , then the derivative of ln(x^2+16) = 1/(x^2+16)*2x . Now if we multiply 2x by the constant 500 we get 1000x .