| 
January 13th, 2009, 08:24 PM
| | Newbie | | Join Date: Jan 2009
Posts: 8
Country:  Thanks: 11
Thanked 0 Times in 0 Posts
| |  Major Integration Help
A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! |
January 13th, 2009, 08:46 PM
| | MHF Contributor | | Join Date: Aug 2008
Posts: 1,525
Country:  Thanks: 48
Thanked 603 Times in 565 Posts
| |
Quote:
Originally Posted by dillonmhudson  A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! | 1. Are you sure the numerator isn't  ???
__________________
Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe... | | The following users thank Prove It for this useful post: | |  |
January 13th, 2009, 08:50 PM
| | MHF Contributor | | Join Date: Aug 2008
Posts: 1,525
Country: Thanks: 48
Thanked 603 Times in 565 Posts
| |
Quote:
Originally Posted by dillonmhudson A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! | 1. Long divide. Then the integrand becomes  . Much easier.
__________________
Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe... | | The Following 2 Users Say Thank You to Prove It For This Useful Post: | | |
January 13th, 2009, 08:51 PM
| | Newbie | | Join Date: Jan 2009
Posts: 8
Country: Thanks: 11
Thanked 0 Times in 0 Posts
| |
You thinking about factoring? Yeah I'm positive, I double checked that. |
January 13th, 2009, 08:52 PM
| | MHF Contributor | | Join Date: Aug 2008
Posts: 1,525
Country: Thanks: 48
Thanked 603 Times in 565 Posts
| |
Quote:
Originally Posted by dillonmhudson You thinking about factoring? Yeah I'm positive, I double checked that. | Worth a shot.
You'll have to long divide in that case.
__________________
Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe... | | The following users thank Prove It for this useful post: | | |
January 13th, 2009, 08:54 PM
| | MHF Contributor | | Join Date: Aug 2008
Posts: 1,525
Country: Thanks: 48
Thanked 603 Times in 565 Posts
| |
Quote:
Originally Posted by dillonmhudson A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! | 3. Remember that  .
Make the substitution  .
__________________
Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe... | | The Following 2 Users Say Thank You to Prove It For This Useful Post: | | |
January 13th, 2009, 08:56 PM
| | MHF Contributor | | Join Date: Aug 2008
Posts: 1,525
Country: Thanks: 48
Thanked 603 Times in 565 Posts
| |
Quote:
Originally Posted by dillonmhudson A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! | For 5. You'll have to long divide as well.  .
__________________
Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe... | | The following users thank Prove It for this useful post: | | |
January 13th, 2009, 09:00 PM
|  | Senior Member | | Join Date: Nov 2008 Location: Moscow
Posts: 352
Country:  Thanks: 17
Thanked 195 Times in 158 Posts
| |
Quote:
Originally Posted by dillonmhudson A lot of question on some really hard homework I have. Any help would be greatly appreciated. Thanks.
1. int [ (x^2 - 3x + 2) / (x+1) * dx ]
2. int [ x^(1/2) / (x^(1/2) - 3) * dx ]
3. int [ tan 5x * dx ]
___An even problem, is the answer:
___-ln | csc(2x) + cot(2x) | + c
4. int [ sec (x/2) * dx ]
___An even problem, is the answer:
___2*ln | sec(x/2) + tan(x/2) | + c
5. int 2/0 [ (x^2 - 2) / (x + 1) * dx ]
Thanks Again! | ![1.{\text{ }}\int {\frac{{{x^2} - 3x + 2}}{{x + 1}}} dx = \int {\frac{{\left( {x + 1} \right)x - \left( {4x - 2} \right)}}{{x + 1}}} dx = \int {\left[ {x - \frac{{4x - 2}}{{x + 1}}} \right]} dx =](http://www.mathhelpforum.com/math-help/latex2/img/1cea32b4b3aba0189693346ff7bb3067-1.gif "1.{\text{ }}\int {\frac{{{x^2} - 3x + 2}}{{x + 1}}} dx = \int {\frac{{\left( {x + 1} \right)x - \left( {4x - 2} \right)}}{{x + 1}}} dx = \int {\left[ {x - \frac{{4x - 2}}{{x + 1}}} \right]} dx =") ![= \frac{{{x^2}}}{2} - 2\int {\frac{{2x - 1}}{{x + 1}}} dx = \frac{{{x^2}}}{2} - 2\int {\frac{{2x + 2 - 3}}{{x + 1}}} dx = \frac{{{x^2}}}
{2} - 2\int {\left[ {2 - \frac{3}{{x + 1}}} \right]} dx =](http://www.mathhelpforum.com/math-help/latex2/img/c882c1897e1fe3426568530b655b0457-1.gif "= \frac{{{x^2}}}{2} - 2\int {\frac{{2x - 1}}{{x + 1}}} dx = \frac{{{x^2}}}{2} - 2\int {\frac{{2x + 2 - 3}}{{x + 1}}} dx = \frac{{{x^2}}}
{2} - 2\int {\left[ {2 - \frac{3}{{x + 1}}} \right]} dx =")  | | The Following 2 Users Say Thank You to DeMath For This Useful Post: | | |
January 14th, 2009, 01:21 PM
|  | Math Engineering Student | | Join Date: Mar 2007 Location: Santiago
Posts: 3,056
Country:  Thanks: 82
Thanked 1,362 Times in 1,086 Posts
| |
Quote:
Originally Posted by DeMath | Not quite on the  something is missing...  | | The Following 2 Users Say Thank You to Krizalid For This Useful Post: | | |
January 14th, 2009, 01:39 PM
| | Senior Member | | Join Date: Nov 2008 Location: Moscow
Posts: 352
Country: Thanks: 17
Thanked 195 Times in 158 Posts
| |
| | The following users thank DeMath for this useful post: | | |
January 14th, 2009, 02:47 PM
| | Newbie | | Join Date: Jan 2009
Posts: 18
Country: Thanks: 11
Thanked 3 Times in 3 Posts
| |
Quote:
Originally Posted by Prove It 1. Long divide. Then the integrand becomes . Much easier. | I think the integrand should be  after the long division. | | The following users thank stevedave for this useful post: | | | | Thread Tools | | | | Display Modes |  Linear Mode | 
Posting Rules
| You may not post new threads You may not post replies You may not post attachments You may not edit your posts
HTML code is Off | | | All times are GMT -7. The time now is 08:13 AM. | | |
