7.1 Integration By Parts/51: Revision history

29 November 2022

• curprev 03:5503:55, 29 November 2022‎ Elizabethh58413 talk contribs‎ 658 bytes +658‎ Created page with "<math> \text{use Exercise 47 to evaluate} \int(\ln{x})^3dx </math> <br><br> <math> \text{Exercise 47:}\qquad x(\ln{x})^n-n\int(\ln{x})^{n-1}dx </math> <br><br> <math> \int(\ln{x})^3dx= x(\ln{x})^3-3\int(\ln{x})^2dx </math> <br><br> <math> u = (\ln{x})^2 \qquad dv = dx </math> <br><br> <math> du = 2\frac{1}{x}\ln{x}dx \qquad v = x </math> <br><br> <math> \begin{align} \int(\ln{x})^3dx &= x(\ln{x})^3-3\int(\ln{x})^2dx = x(\ln{x})^3-3[x(\ln{x})^2 - 2\int(\ln{x})dx] \\[2e..."