- #1
clairez93
- 114
- 0
Homework Statement
[tex]\int\frac{t^{2}}{\sqrt{2+3t}}[/tex]
Use integration by parts to verify the formula:
[tex]\int x^{n} sin x dx = -x^{n} cos x + n\int x^{n-1} cos x dx[/tex]
Homework Equations
The Attempt at a Solution
For the first one, I attached the picture of my work on paper, as it would take me forever to type out in latex code, I think. For the second one:
[tex]u = sin x[/tex]
[tex]du = cos x[/tex]
[tex]dV = x^{n}[/tex]
[tex]V = \frac{x^{n+1}}{n+1}[/tex]
[tex]\int x^{n} sin x dx = -x^{n} cos x + n\int x^{n-1} cos x dx[/tex] =
[tex]sin x (\frac{x^{n+1}}{n+1}) - \int \frac{x^{n+1}}{n+1} cos x dx[/tex]
That doesn't really look like the formula to me. Am I supposed to use an identity of some sorts?