Definite and Indefinite Integral help

[drew51]

Hey All,

I need the indefinite integral of 2 problems and can you please show it step by step so I can learn how to do these.

First indefinite integral of e^t / (1-e^t)² dt

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Second is the definite integral where b = 2 and a = 1 of e ^(1/x) / x² dx

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Bonus Question (you do not have to do this)

Calculate the volume of the solid obtained by rotating the region bounded by
y=x⁴, y= 0, x= 1 about the line x= 2. This i assume has to do with Washers?

Thank You all who attempt, I really appreciate it

 

[Deleted member 4993]

Hey All,

I need the indefinite integral of 2 problems and can you please show it step by step so I can learn how to do these.

First indefinite integral of e^t / (1-e^t)² dt

---

Second is the definite integral where b = 2 and a = 1 of e ^(1/x) / x² dx

---

Bonus Question (you do not have to do this)

Calculate the volume of the solid obtained by rotating the region bounded by
y=x⁴, y= 0, x= 1 about the line x= 2. This i assume has to do with Washers?

Thank You all who attempt, I really appreciate it

Hints:

First indefinite integral of e^t / (1-e^t)² dt

substitute → u = 1- e^t → du = -e^t dt

Second is the definite integral where b = 2 and a = 1 of e ^(1/x) / x² dx

substitute → u = e^(1/x) → du = - (1/x²) * e^(1/x) dx ......................................edited

Now continue.....

Please share your work with us .

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