your answer is C I'm definitely sure
102% of 250 = 255 Hope this helps ( :
Answer:
1. 3/2
2. 4
Step-by-step explanation:
![\int e^{x/2} /(e^{x/3} +1) dx](https://tex.z-dn.net/?f=%5Cint%20e%5E%7Bx%2F2%7D%20%2F%28e%5E%7Bx%2F3%7D%20%2B1%29%20dx)
start with substituting z=e^x
![z=e^x\\dz=e^x dx\\\int \frac{dz}{z^{5/6}+z^{1/2}}](https://tex.z-dn.net/?f=z%3De%5Ex%5C%5Cdz%3De%5Ex%20dx%5C%5C%5Cint%20%5Cfrac%7Bdz%7D%7Bz%5E%7B5%2F6%7D%2Bz%5E%7B1%2F2%7D%7D)
then substitute u = z^(1/6):
![u=z^{1/6}\\dz=6 z^{5/6}du\\6 \int \frac{u^2}{u^2+1}du](https://tex.z-dn.net/?f=u%3Dz%5E%7B1%2F6%7D%5C%5Cdz%3D6%20z%5E%7B5%2F6%7Ddu%5C%5C6%20%5Cint%20%5Cfrac%7Bu%5E2%7D%7Bu%5E2%2B1%7Ddu)
that integral has a standard form that can be looked up in integral tables, it has the following solution:
![6(u - \tan^{-1} u) + \mbox{constant}](https://tex.z-dn.net/?f=6%28u%20-%20%5Ctan%5E%7B-1%7D%20u%29%20%2B%20%5Cmbox%7Bconstant%7D)
substituting back the the variable z and then x you get the final solution:
![6 e^{x/6} - 6 \tan^{-1}(e^{x/6}) + \mbox{constant}](https://tex.z-dn.net/?f=6%20e%5E%7Bx%2F6%7D%20-%206%20%5Ctan%5E%7B-1%7D%28e%5E%7Bx%2F6%7D%29%20%2B%20%5Cmbox%7Bconstant%7D)
Answer:
-
Step-by-step explanation:
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