3.6.E: Exercises
- Page ID
- 157590
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In problems 1–4, a function \(u\) or \(dv\) is given. Find the piece \(u\) or \(dv\) which is not given, calculate \(du\) and \(v\), and apply the Integration by Parts Formula.
| 1. \(\int 12x \cdot \ln(x) dx\) | \(u = \ln(x)\) | 2. \(\int x \cdot e^{–x} dx\) | \(u = x\) |
| 3. \(\int x^4 \ln(x) dx\) | \(dv = x^4 dx\) | 4. \(\int x \cdot (5x + 1)^{19} dx\) | \(u = x\) |
In problems 5 - 10 evaluate the integrals
| 5. \(\int^1_0 \frac{x}{e^{3x}} dx\) | 6. \(\int^1_0 10x \cdot e^{3x} dx\) | 7. \(\int^3_1 \ln (2x + 5) dx\) |
| 8. \(\int x^3 \ln (5x) dx\) | 9. \(\int x \ln (x + 1) dx\) | 10. \(\int^2_1 \frac{\ln (x)}{x^2} dx\) |
For problems 11 - 14 integrate each function.
| 11. \(\int \frac{1}{4-x^2}\) | 12. \(\int \frac{2}{9-x^2}\) | 13. \(\int \sqrt{4+x^2}\) | 14. \(\int \sqrt{9+x^2}\) |