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What is the antiderivative of #ln(1+x)#?

1 Answer

Konstantinos Michailidis

Mar 10, 2016

The antidervative is #x*ln(1+x)-x+ln(1+x)+c#

Explanation:

The antiderivative of #ln(1+x)# is the integral

#int ln(1+x)dx=int x' *ln(1+x)dx=x*ln(1+x)-int x/(1+x)dx= x*ln(1+x)-int[1-1/[1+x]]dx= x*ln(1+x)-x+ln(1+x)+c#

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