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Solution: ∫ln(xⁿ)/x*dx = n*∫ln(x)*x^(-1)*dx = ------------------------------------ Solution by partial integration: Partial integration can be derived from the product rule of differential calculus. The product rule of differential calculus states: (u*v)’ = u’*v+u*v’ |-u’*v ⟹ (u*v)’-u’*v = u*v’ ⟹ u*v’ = (u*v)’-u’*v |∫() ⟹ ∫u*v’*dx = u*v-∫u’*v*dx ------------------------------------ n*∫ln(x)*1/x*dx = n*ln²(x)-n*∫1/x*ln(x)*dx |+n*∫1/x*ln(x)*dx ⟹ 2*n*∫ln(x)*1/x*dx = n*ln²(x)+C |/2 ⟹ n*∫ln(x)*1/x*dx = ∫ln(xⁿ)/x*dx = n/2*ln²(x)+C/2 Checking the result by deriving: [n/2*ln²(x)+C/2]’ = n*ln(x)*1/x = ln(xⁿ)/x everything okay!

BUT that doesn't mean there is no such thing as an even or odd NUMBER

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It’s 1.

Thanks ❤

good

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ey what is the meaning of s btw

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ln(1/8)=ln(1/2³) =ln(2`³) using power rule =-3ln(2)

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Respect

actually it’s an isosceles triangle

Foarte frumos explicat fără cuvinte și foarte frumos ilustrat. Succes în continuare.

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Put lnx=z

Thank you. The solution leaves an aftertaste - as it is not really beautiful or elegant, it does not “feel” like a solution. There is a psychological question: when is something a solution ? Anyone has an opinion ?

The equation is split between three terms, 3-(4x0)-(4/4). Simplifying with pemdas gets 3-0-1 which equals 2. 2 is the answer

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First, try to solve the problem, then see the answer in the link below: ruclips.net/video/3djrXiO0lHY/видео.htmlsi=y5w6FivAkkoNGB8E

The answer is nonelementary, but if you want that function would be li(x)+C where li(x) is a logarithmic integral function.

utterly magical

Lnx cosx ;

Πουτσα

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Excellent❤

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