Grade 12Integral Calculus
what is the integration of (log x)/x and give solutions too ?
what is the integration of (log x)/x and give solutions too ?
2 Answers
Rohit
You can put log x as u and solve the following question and afterward you have to substitute the vale of u in the equation and
there you have the answer to your question. This is the strating part of integration. So practice hard and do well
∫ log x/x dx.
Let u = log x.
Then du = dx/x.
So it becomes
∫ u du = u²/2
So it becomes
∫ u du = u²/2
=(log x)²/2 + C
I think it would surely help you out
Regards
John
Using integration by parts ($udv=uv-$vdu(Inx/x)dxLet u=Inx and dv=1/xSo that du=1/x dx and v=Inx Therefore(Inx/x)dx= uv-$vdu = Inx•Inx-$Inx•1/x dx =(Inx)^2 -$(Inx/x) dx I=(Inx)^2 - I I+I=(Inx)^22I=(Inx)^2Divide both sides by 2I= (Inx)^2/2 +C
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