MATH3503 Online Assignment 6

• Make sure to use the link on the Learning Hub, which contains a user name and a user ID unique to you, otherwise your mark would not be recorded. You may use the URL without '?uname=...&uid=...' if you just want to practice. You will get different numbers every time you open the page.
• Numerical answers are evaluated as correct if the difference from the correct value is less than `0.001 times` (correct value) unless otherwise specified. That means, you need to keep at least 5 significant digits (e.g., 12.34, 0.01234, etc.) in your final answer, and a couple of more digits in the intermediate steps.

Integration by Parts

1.  
   `int x e^{-4x}dx=``+C`
   
   
   
2.  
   `int x^2 e^{4x}dx=``+C`
   
   
   
3.  
   `int x^{5}cos(3x^{3})dx =``+C`
   * Hint: Try substitution `u = 3x^{3}`.
   
   
4.  
   \(\displaystyle\int x^{3/5}\ln x\ dx =\)`+C`
   
   
   
5.  
   \(\displaystyle\int \arcsin(8x)\,dx =\)`+C`
   * Hint: There is always an invisible 1. Use asin(x) for `arcsin(x)`.
   
   
6.  
   \(\displaystyle\int x\sec^2(6x)\,dx =\)`+C`
   * Hint: `tan x = (sin x)/(cos x)`. Use integration by parts.
   
   
7.  
   \(\displaystyle\int e^{3x}\sin(5x)\,dx =\)`+C`
   
   
   

If you are ready to submit the result, click Submit!   *Make sure that all questions are evaluated. Click "Check answers!" before clicking "Submit!".