Question

solve..integration sign--> S (2+ln u )/u^2 by substitution u = e^x

Answer 1

this one?

Answer 2

yep

Answer 3

since u = e^x; what does u' equal?

Answer 4

e^x i guess

Answer 5

yep, so we need to substitute in all the proper parts

\[\int \frac{2+ln(u)}{u^2}du\]
\[u=e^x\]\[du = e^x~dx\]

\[\int \frac{2+ln(e^x)}{(e^x)^2}e^x~dx\]
can you simplify that ?

Answer 6

how did you get e^x dx

Answer 7

it is given that

u=e^x ; to find out what du equals, we have to take the derivative of u

Answer 8

thnx i got it
i was jst missing e^x dx part therefore getting wrong answer
may thnx

Answer 9

many thnx

Answer 10

\[\frac d{dx}(u=e^x)\]
\[\frac d{dx}(u)=\frac d{dx}(e^x)\]
\[\frac {du}{dx}=e^x\]
\[du=e^x~dx\]

Answer 11

yeah, you gotta make sure you are replacing all the u parts with their correct x counter parts ;)

good luck