Mathe: Integralrechnung

[Christoph]

Moin.

Es gilt
[latex]\frac{x-c}{x+1}\bold{d}x = \left(\frac{x+1}{x+1}-\frac{c+1}{x+1}\right)\bold{d}x[/latex]
[latex]= \bold{d}x - (c+1)\frac{1}{x+1}\bold{d}(x+1)[/latex]
[latex]= \bold{d}x - (c+1)\bold{d}\ln{|x+1|}[/latex]
und damit
[latex]\int_a^b \frac{x-c}{x+1}\bold{d}x = b-a - (c+1)(\ln{|b+1|}-\ln{|a+1|})[/latex]

Christoph