Solving Substitution Problem: \int (x2 +2x +1)e^(-ln(x+1)) dx

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In summary, the problem involves finding the integral of (x2 +2x +1)e^(-ln(x+1)) dx. The attempt at a solution involves factoring the integrand and making a substitution, but the method for solving is still uncertain. The poster also inquires about responding to answers and whether the person will be notified.
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maff is tuff
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Homework Statement



[tex]\int[/tex] (x2 +2x +1)e^(-ln(x+1)) dx


Homework Equations






The Attempt at a Solution



I started off by factoring the integrand into:

[tex]\int[/tex] (x+1)(x+1)e^(-ln(x+1)) du

Then I tried to make a substitution:

u=(x+1) so du=dx

This left me with this:

[tex]\int[/tex] u2 e^(-lnu) du

So now do I use integration by parts or something? Thanks in advance for the help. And also, if someone responds to my question and I want to respond back, do I just reply to this same thread or PM the person who responded? I ask this because I don't know if I were to reply to this thread if the person will be notified or not. Thanks again.
 
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FAQ: Solving Substitution Problem: \int (x2 +2x +1)e^(-ln(x+1)) dx

How do I solve this substitution problem?

To solve this substitution problem, you will need to use the substitution method in integration. Start by letting u = ln(x+1), then take the derivative of u to get du = 1/(x+1) dx. You can then substitute u and du into the integral and integrate as usual.

What is the purpose of using substitution in integration?

Substitution allows us to simplify complex integrals by replacing parts of the function with a new variable. This makes it easier to integrate and find the solution.

Can I use any substitution variable in an integral?

No, the substitution variable must be a function of the original variable and its derivative must also appear in the integral. In this case, u = ln(x+1) satisfies both requirements.

What is the importance of using the exponential function in this substitution problem?

The exponential function e^u is used in this substitution problem because it is the inverse of the natural logarithm function, which is present in the integral. This allows us to cancel out the natural logarithm and simplify the integral.

Can I use substitution in all integration problems?

No, substitution is not always necessary or applicable in integration problems. It is usually used to simplify integrals that involve complicated functions or expressions. In simpler integrals, it may not be needed.

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