verifying eulers theorem for homogeneous functions ?

if f(x,y) = x² cos(x/y) + 3xy , show that f satisfies



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partial fractions

put 1/ [x(1 + x ² )] into partial fractions

other examples
put into partial fraction 1 / {(x^3) + 1 } -----> (partial fractions problem)

put 1/[ (x)(x-2)(2x-1)] into partial fractions ----------partial fraction


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integral of ln(x) using integration by parts

find the integral of ln(x)

make it into ln(x )*1 {remember ILATE rule} and then start off integration by parts
some other examples
integral of (e^(ax))cosbx using integration by parts ----------> (integration by parts)

.∫ (x²) sin x dx using integration by parts ----------> (integration by parts)

integral of { sqrt{1+x^2} } / {x^2} using integration by parts ----------> (integration by parts)

∫ arc(tan4x) dx ----------> (integration by parts)

other examples on problems in math --------math problems

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integration by substitution

evaluate integral of e^(2x) / sqrt [1 + e^(2x)]

some other examples
integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution

integral of e^{x^(1/3)}-------------- e^{x^(1/3)}

integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution

more problems on integration -----------problems on integration

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evaluate .∫ [1 / {x lnx}]dx

evaluate ∫ [1 / {x lnx}]dx

put u = lnx find du, substitute into the given integral and then
evaluate





another example
evaluate integral of { e^(1 /x^2)} / {x^3} substitution

integration formulae



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