Question

integration by parts with a definite integral: Simplified the definite integrate, but I'm having problems with plugging in the limits and evaluating the problem from there. I'll post my answer, so far, and the original problem in the next post.

Answer 1

Original problem:
\[\int\limits_{1}^{e^2}x^2\ln(x)dx\]

My Solution so far:
\[x^3/3\ln(x) - x^3/9+C\]

^ Note: The first fraction should be a x^3/3

Answer 2

That's right, now;
\[ \frac{x^3}{3}Ln(x)-\frac{x^3}{9}|_{1}^{e^2}= \frac{(e^{2})^{3}}{3}Ln(e^2)-\frac{(e^2)^3}{9} \;\;\;-[\frac{1^{3}}{3}Ln(1)-\frac{(1)^3}{9}]=\frac{2e^{6}}{3}-\frac{e^{6}}{9}\;\;-[0-\frac{1}{9}]\]
which is
\[\frac{5e^6+1}{9}\]

Answer 3

the last number on the right is -1/9

Answer 4

wherre did you get the five from?

Answer 5

Find common denominator....which is nine, multiply first term by 3 on top and bottom, so you get 6e^2-1e^6=5e^5

Answer 6

5e^6