Hello,
In mathematica,
I tried to find
Integral of ln(1 + x)/(x^2 + 1) from 0 to 1
The answer is CLEARLY ln(2)pi/8
Mathematica computes the answer to be:
1/4 ln ([Pi] + Log[4])
Which is incorrect. Why is Mathematica computing this error??
That is interesting. I typed in
Integrate[Log[(1 + x)]/(x^2 + 1), {x, 0, 1}]
which gives
which is as you state: CLEARLY correct. I tried a while and did not find what could make Mathematica produce the output you report.
M.
?ln
It’s impossible to cut and paste an image. It appears that this is your computation:
Integrate[ln*(1+x)/(1+x^2), {x,0,1}]
If so, you are making some erroneous assumptions. One is that “ln” and “Log” are viewed as the same entity in Mathematica. Another is that you are using correct syntax for what is, in Mathematica, Log[x+1]. Yet another is that the mistake, such as it is, is in the program and not the use thereof.
A general rule in software is as follows: blame the program after rather than before checking documentation, and even then consider the possibility that you may have missed something.
The correct syntax is Integrate[ Log[1+x]/(x^2+1), {x, 0, 1}]. The only problem here was that “Log” is the correct form of “ln”. You may have received the incorrect answers based on some prior definitions. It is mostly a good idea to clear memory before starting fresh computations, with Clear["Global*"]or at leastClearAll[variablename]` if the variable name is known.
Hi,
But how can this work if I want to FIRST input the function, and use the drop down integral option?
Here are some posting basics I will recommend. Think of them as courtesies you might provide to the reader.
(1) Input code instead of an image.
(2) Check the documentation. Mathematica is case sensitive.
(3) When you use a general phrase like “not working”, consider the possibility that it might be working just fine.
(4) Read the responses carefully in order to be sure you are replicating what they show.
It is generally good practice to have a rudimentary familiarity with the software before making claims about bugs.
f[x_] := Log[1+x]/(x^2+1);
Integrate[ f, {x, 0, 1}]
Need Log
Notebook attached.
Nice! Thanks
Capitalize log - should be Log.
A shame I can only give you one vote for this…
I think that your “courtesy rules” should go on
Cheers,
Marco