# Impossible evaluation NEED HELP T_T

• MathNoob123
In summary, To evaluate the integral of 25x^2lnxdx, use substitution twice starting with In (x) as D. The antiderivative of e^(ln(4)*x) is e^(ln(4)*x) all over ln(4)x. There is a trick to simplify the process if you have \int 25x^2\ln x dx, which involves using substitution and integration by parts.
MathNoob123

## Homework Statement

evaluate the integral of 25x^2lnxdx

## The Attempt at a Solution

First thing I did was set 25x^2 as D, then set lnx as I. Derivative of 25x^2 is 50x. The antiderivative of lnx is xlnx-x. Therefore it turned out to be something like...25x^2(xlnx-x)-integral of 50x(xlnx-x). Then i proceeded by finding the antiderivative of my second integral...but soon found out that its an unending process if this keeps going up. PLEASE HELP. ADVICE IS REALLY APPRECIATED. THANK YOU SO MUCH.

You need to use substitution twice. Start with In (x) as D

rootX said:
You need to use substitution twice. Start with In (x) as D

alright Ill try that, thanks for the advice. And by the way do you perhaps know the antiderivative of e^(ln(4)*x)? Because on this one certain problem i had to find the antiderivative of 4^x which i found to be e^(ln(4)*x) but i can't seem to know how to find the antiderivative of e^(ln(4)*x). Is it perhaps e^(ln(4)*x) all over ln(4)x?

thank you for taking your time to help me out. Really appreciate it.

Isn't this like the third thread out of 5 top ones that ask the same question?

MathNoob123 said:
First thing I did was set 25x^2 as D, then set lnx as I. Derivative of 25x^2 is 50x. The antiderivative of lnx is xlnx-x. Therefore it turned out to be something like...25x^2(xlnx-x)-integral of 50x(xlnx-x). Then i proceeded by finding the antiderivative of my second integral...but soon found out that its an unending process if this keeps going up. PLEASE HELP. ADVICE IS REALLY APPRECIATED. THANK YOU SO MUCH.

There's a nice little trick here if you realize you have:

$$\int 25x^2\ln x dx=25x^2(x\ln x -x)-\int50x^2\ln x dx +\int 50x^2 dx$$

$$\implies \int 50x^2 \ln x dx+ \int 25x^2\ln x dx=3\int 25x^2\ln x dx=25x^2(x\ln x -x)+\int 50x^2 dx$$

$$\implies\int 25x^2\ln x dx=\frac{1}{3}\left(25x^2(x\ln x -x)+\int 50x^2 dx\right)$$

## 1. What is "Impossible evaluation"?

"Impossible evaluation" refers to the process of evaluating something that is considered impossible or extremely challenging to achieve. This can refer to evaluating a problem, a theory, or an experiment.

## 2. Why is "Impossible evaluation" important?

"Impossible evaluation" is important because it challenges our current understanding and pushes the boundaries of what is considered possible. It can lead to new discoveries and advancements in science and technology.

## 3. How is "Impossible evaluation" different from other types of evaluation?

"Impossible evaluation" differs from other types of evaluation in that it often requires unconventional thinking and approaches. It involves tackling problems and theories that may seem impossible to solve or prove.

## 4. What are some examples of "Impossible evaluation" in science?

Some examples of "Impossible evaluation" in science include trying to find a cure for incurable diseases, finding ways to travel faster than the speed of light, and attempting to understand the concept of time travel.

## 5. How can scientists approach "Impossible evaluation"?

To approach "Impossible evaluation," scientists must be open-minded, creative, and persistent. They must be willing to challenge existing beliefs and think outside the box. Collaboration and interdisciplinary research can also be helpful in tackling seemingly impossible problems.

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