A level, Further Maths, integration question

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sodko
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Can you solve integration of (ln(x)/(x+5))dx in the interval of 1 and the infinity
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TSR Jessica
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JirachiPark
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(Original post by sodko)
Can you solve integration of (ln(x)/(x+5))dx in the interval of 1 and the infinity
Hi sodko!

You wouldn't be able to evaluate the function (ln(x)/(x+5)) between 1 and infinity because the graph of this function doesn't converge (it is divergent).

If d/dx(ln(x))^2=2xln(x) then

∫(1/x)ln(x)dx between 1 and a

=1/2((ln(a))^2−(ln(1))^2)=1/2(ln(a))^2

but ln(a) is a monotonic strict increasing function of a (one that increases as x does for all real x) so
lim a→∞∫(1/x)lin(x)dx (between 1 and a) =∞

so it is not convergent.

Hope this helps,

Aaron
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sodko
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(Original post by JirachiPark)
Hi sodko!

You wouldn't be able to evaluate the function (ln(x)/(x+5)) between 1 and infinity because the graph of this function doesn't converge (it is divergent).

If d/dx(ln(x))^2=2xln(x) then

∫(1/x)ln(x)dx between 1 and a

=1/2((ln(a))^2−(ln(1))^2)=1/2(ln(a))^2

but ln(a) is a monotonic strict increasing function of a (one that increases as x does for all real x) so
lim a→∞∫(1/x)lin(x)dx (between 1 and a) =∞

so it is not convergent.

Hope this helps,

Aaron
Thank you so much
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