evaluate-lnx-dx-

Question Number 73545 by Rio Michael last updated on 13/Nov/19

e v a l u a t e \int l n x d x

Commented by Tony Lin last updated on 13/Nov/19

i n t e g r a t i o n b y p a r t

\int f^{'} (x) g (x) = f (x) g (x) - \int f (x) g^{'} (x)

\int l n x d x

= \int (1 \times l n x) d x

= x l n x - \int (x \times \frac{1}{x}) d x

= x l n x - x + c

Commented by Rio Michael last updated on 13/Nov/19

t h a n k s

Answered by ajfour last updated on 13/Nov/19

\frac{d}{d x} (x \ln x) = \ln x + 1

\Rightarrow d (x \ln x) = (\ln x) d x + d x

I n t e g r a t i n g

\int d (x \ln x) = \int (\ln x) d x + \int d x

x \ln x + c = \int (\ln x) d x + x

\Rightarrow \int \ln x d x = x \ln x - x + c .

Commented by Rio Michael last updated on 13/Nov/19

i a p p r e c i a t e s i r