Frage zur Substitution: Integral von 2 bis +inf: 1/(x(lnx^2)dx. Folgende Substitution: u=lnx --> mit dieser Substitution führt meine Uni Professorin an: Integral von ln2 bis +inf: 1/u^2. wieso ist 1/u^2 das selbe wie 1/x(lnx^2) mit dieser substitution?
Frage zur Substitution: Integral von 2 bis +inf: 1/(x(lnx^2)dx. Folgende Substitution: u=lnx --> mit dieser Substitution führt meine Uni Professorin an: Integral von ln2 bis +inf: 1/u^2. wieso ist 1/u^2 das selbe wie 1/x(lnx^2) mit dieser substitution?
Please understand that I only speak English:)
∫∞21x(ln(x2))dx=∫∞212xlnxdx letu=lnxx=eudxdu=eudx=eudu =∫∞212xlnxdx=∫∞212euu×eudu=∫∞212udu=12∫∞21udu=12[lnu]∞2
This integral does not converge so the answer is infinite
You must mean somthing different - Maybe.....
∫∞21x(ln2(x))dx letu=lnxx=eudxdu=eudx=euduand when x=2u=ln2 when x=∞u=ln(∞)=∞ ∫∞ln21x(ln2(x))dx=∫∞ln21euu2×eudu=∫∞ln21u2du=∫∞ln2u−2du=[u−1−1]∞ln2=[−1u]∞ln2=0−−1ln2=1ln2
That is more like it :)
Thanks Melody. Super fast and super clean answere, cheers for that :)
i did mean the first case you calculated, and now i noticed that my (sometimes) confused Professor just messed up the writing. She should have written: 1/xln^2x, she did write: 1/xln(x^2). Did just notice that 'cause you said "does not converge" :)
Keep up the good work, Daniel
hi Daniel :)
Your teacher wrote
1/(x(lnx^2)
Which need a closing bracket to start with
1/(x(lnx^2))
but yes she should have written
1/(x(ln^2x)
OR better still in my view would be
1/(x(lnx)^2)
I knew my interpretation was wrong because I did not get the solution that your teach got. :)