ln(2x+1) proof on HP Calculator

[Athanasios]

Hi,

I am attempting to solve the proof ∫ ln(2x+1)dx using the HP Prime Calculator.

When I solve the proof by had my solution is as follows:

{(2x+1)/2} * ln(2x+1) - x + C

However, when I use the HP Prime I end up with the following solution:

There is a constant of -1/2 (highlighed in yellow) which I do not understand.

Can someone please explain to me why/how there is a constant value of -1/2 in the calculator derived answer?

Thanks,

Athanasios

[Maké · Accepted solution]

Hi!, @Athanasios:

See, the image of Wolfram Alpha, with alternate form, is same, but change, the order, if you simplify in the HP PRIME. 

[Jan_D]

Your own solution is correct and the general solution, but the intergral function without boundaries does not give constants, because these are trivial.

So you have to add a constant C2 to it and then you get the same because C=C2-1/2.