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

Question

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

amistre64 · Answer

this one?

anonymous · Answer

yep

amistre64 · Answer

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

anonymous · Answer

e^x i guess

amistre64 · Answer

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 ?

anonymous · Answer

how did you get e^x dx

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

many thnx

amistre64 · Answer

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

amistre64 · Answer

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