If $$\int_{0}^{\infty}\frac{\ln x dx}{x^2+e^2}=k$$ then what is $[k]$=?
The thing is I cant evaluate even 'k'! Please help me with this. Thanks in advance.
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Do the substitution as $x=\frac{e^2}{t}$. Separate the terms in it. Change the limits and all. See what you get. You can actually solve for the integral.
$$\int_0^{\infty}\frac{2-\ln(t)}{e^2+t^2}dt$$
Now I hope you can solve it. Second term is the integral you want.
Dhanush Krishna
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1but x is the variable – Apr 09 '16 at 15:45
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Yes, since it is a variable you can replace it. See http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleDefinite.aspx or some other websites to learn some basic integration techniques. – Dhanush Krishna Apr 09 '16 at 15:47
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2Clever substitution! +1 – Plutoro Apr 09 '16 at 15:50
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@IanMiller: Yes I meant the first one. – Dhanush Krishna Apr 09 '16 at 15:56
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@DhanushKrishna I was commenting on the 'u' (which was mistyped by you) instead of 'x' – Apr 09 '16 at 16:02
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@XBOveRLorD: I am sorry , my bad. – Dhanush Krishna Apr 10 '16 at 04:00