if-ln-x-2-dx-x-ln-2-x-a-ln-x-b-C-a-b-C-are-constant-find-the-value-of-a-and-b-

Question Number 90765 by john santu last updated on 26/Apr/20

i f \int {(\ln (x))}^{2} d x =

x (\ln^{2} (x) + a \ln (x) + b) + C

a, b, C a r e c o n s t a n t .

f i n d t h e v a l u e o f a a n d b

Commented by jagoll last updated on 26/Apr/20

\int f (x) d x = h (x) \Rightarrow f (x) = h^{'} (x)

\ln^{2} (x) = \ln^{2} (x) + a \ln (x) + b +

x (\frac{2 \ln (x)}{x} + \frac{a}{x})

0 = (a + 2) \ln (x) + (a + b)

{\begin{cases} a = - 2 \\ b = 2 \end{cases}

Commented by john santu last updated on 26/Apr/20

g o o d