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Question Number 110619 by mathdave last updated on 29/Aug/20

s o m e o n e p o s t e d t h i s p r o b l e m a n d m y

s o l u t i o n f o l l o w e d

s o l v e

\int_{0}^{1} \frac{\ln (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x

s o l u t i o n

y = \ln (x + \sqrt{1 + x^{2}}) a n d d y = \frac{1}{\sqrt{1 + x^{2}}} d x

a t x = 0, y = 0 a n d a t x = 1, y = \ln (1 + \sqrt{2})

h e n c e

I = \int_{0}^{\ln (1 + \sqrt{2})} \frac{y}{\sqrt{1 + x^{2}}} \times \sqrt{1 + x^{2}} d y = \int_{0}^{\ln (1 + \sqrt{2})} y d y

I = {[\frac{y^{2}}{2}]}_{0}^{\ln (1 + \sqrt{2})} = \frac{1}{2} \ln^{2} (1 + \sqrt{2})

∵ \int_{0}^{1} \frac{\ln (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x = \frac{1}{2} \ln^{2} (1 + \sqrt{2})

Commented by mathdave last updated on 29/Aug/20

w h y d i d y o u m a r k i t r e d . w h a t i s t h a t

s u p p o s e t o m e a n

Commented by Her_Majesty last updated on 30/Aug/20

I {d i d n}^{'} t m a r k i t r e d b u t I c a n t e l l y o u t h e

r e a s o n s o m e o n e d i d :

w e h a v e 3 o p t i o n s t o p o s t

(1) q u e s t i o n s

(2) a n s w e r s

(3) c o m m e n t s

(1) i s t o p o s t q u e s t i o n s

(2) i s t o p o s t a n s w e r s

(3) i s t o p o s t c o m m e n t s

d o n o t p o s t q u e s t i o n s i n (2) o r (3)

d o n o t p o s t a n s w e r s i n (1) o r (3)

d o n o t p o s t c o m m e n t s i n (1) o r (2)

{i t}^{'} s e a s y, {i s n}^{'} t i t ?