cos-sin-1-x-cos-1-sin-x-ln-ln-ln-1-x-x-dx-

Question Number 217755 by Tawa11 last updated on 20/Mar/25

\int \frac{\cos (\sin^{- 1} x) + \cos^{- 1} (\sin x)}{\ln (\ln (\ln (1 + \sqrt{x + \sqrt{x}})} dx

Commented by mr W last updated on 20/Mar/25

y o u c a n e v e n m a k e i t m o r e n i c e

l o o k i n g

\int \frac{\cos (\sin^{- 1} x + e^{\tan x}) + \cos^{- 1} (\sin x + \tanh x)}{\ln (\ln (\ln (1 + \sqrt{x + \sqrt{x}})} dx

t h e r e a r e a l o t o f o t h e r m a t h e m a t i c

f u n c t i o n s a n d s y m b o l s w h i c h c a n

s t i l l b e p u t i n t o t h e f o r m u l a .

Commented by Tawa11 last updated on 20/Mar/25

Hahahahaha!!!

Answered by SdC355 last updated on 20/Mar/25

Hint .

\cos (asin (z)) = \sqrt{1 - z^{2}}

\sin^{2} (θ) + \cos^{2} (θ) = 1

\sin (θ) = \pm \sqrt{1 - \cos^{2} (θ)} and θ = acos (z)

\sin (acos (z)) = \pm \sqrt{1 - \cos^{2} (acos (z))} = \sqrt{1 - z^{2}}

∵ f * f^{- 1} = z {* is function composition operator}

\cos^{- 1} (\sin (z)) = \frac{π}{2} - z

i think no one can solve \int d z \frac{\sqrt{1 - z^{2}} + \frac{π}{2} - z}{\ln (\ln (\ln (1 + \sqrt{z + \sqrt{z}})))}

Commented by Tawa11 last updated on 20/Mar/25

That is serious sir .

Commented by SdC355 last updated on 20/Mar/25

Because \int \frac{\sqrt{1 - z^{2}} + \frac{π}{2} - z}{^{″} \ln {(\ln (\ln (1 + \sqrt{z + \sqrt{z}})))}^{″}}

Answered by Marzuk last updated on 20/Mar/25

N a h b o y . W e m i g h t p u t s o m e f u n c t i o n a c r y l i c

h e r e i t i s .

\int \frac{(λ x . Γ (x) + β (x, x + 1) + Θ (x) + α (x) . ℜ (e^{i {c o s}^{- 1} x}) + \frac{\partial}{\partial x} [Γ (x) + β (x, x + 1) + Θ (x)}{l n (l n (l n (1 + 2 \sqrt{x}))) + {c o s h}^{- 1} (1 + x^{2}) \int_{0}^{x} \frac{d t}{1 + t^{2}} d e t (\begin{matrix} x c o s (x) \\ s i n (x) x^{2} \end{matrix}) + ψ (x) + Θ (x) + α (x)} d x

N o w t h e p a i n t i n g i s p e r f e c t

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