AMP Parsing Error of [int((sec^2x*dx)/((2+tanx)(3-tanx)))]: Invalid function '\x*dx)/((2+tanx)(3-tanx)))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
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[Your hint says to use t = tanx, but most teachers and books use
the letter u rather than the letter t, so I'll use u = tanx, but 
you can substitute t everywhere I have u if you like.]

let , then AMP Parsing Error of [du = sec^2xdx]: Invalid function '\xdx': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
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, AMP Parsing Error of [dx=du/(sec^2x)]: Invalid function '\x)': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
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AMP Parsing Error of [int((sec^2x*(du/(sec^2x)))/((2+u)(3-u)))]: Invalid function '\x*(du/(sec^2\x)))/((2+u)(3-u)))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
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AMP Parsing Error of [int((cross(sec^2x)*(du/(cross(sec^2x))))/((2+u)(3-u)))]: Invalid function '\x)*(du/(cross(sec^2\x))))/((2+u)(3-u)))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
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Break  into partial fractions:

But before doing that let's get the denominators in descending 
powers of u.
[That isn't absolutely necessary but it is customary because it 
keeps things more orderly.  Also it is customary to get the 
leading term positive, which I will do on the second term]

2+u = u+2      <--first term, just turn it around

3-u = -u+3 = -(u-3)    <--second term, factor out -1









This has to be identically true for all u so substitute u=3
to make the first term on the right become 0







substitute u=-2 to make the second term on the right become 0:









So our integral is now

  



Substitute 



Edwin