How Can You Integrate (4X^3-7X^2+6X-3)/(X^6-4X^3) by Hand?

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In summary, the conversation discusses how to integrate a complex expression by hand and the use of partial fractions. The speaker initially struggled with the integration, but later realized their mistake in simplification.
  • #1
thharrimw
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How colud you intergrate (4X^3-7X^2+6X-3)/(X^6-4X^3) by hand (my TI-89 gave me -[2(13*2^(1/3)-12)(√3*2^(1/3))X^2*Arctan[√3-*2^(1/3)(2X+2^(2/3))/6]+2^(2/3)+28√2+13)X^2ln(X62+2^2/3X+X^(4/3)+2(2^(1/3)(14*2^(2/3)*X^2ln|X-2^(2/3)|-6(14X^2ln|X|)+2(4X-1)))))]\96X^2
i tryed to use partial fractions but i couldn't solve it using partial fractions so i have no idea of where to start.
 
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  • #2
partial fractions works fine, what went wrong?
 
  • #3
never mind I messed up on my simplification i put a extra variable when i simplified so i got
0=A+E,
4=B+D,
-7=C-4E,
6=4D+E,
-3=-4c+A,
insted of
0=A+E,
4=B+D,
-7=C-4E,
6=4D,
-3=-4c,
 

FAQ: How Can You Integrate (4X^3-7X^2+6X-3)/(X^6-4X^3) by Hand?

What is the process for solving a polynomial equation by hand?

The process for solving a polynomial equation by hand involves identifying the degree of the polynomial, grouping like terms, using the distributive property to simplify the equation, and then using algebraic techniques such as factoring or the quadratic formula to find the solutions.

What is the degree of the polynomial 4X^3-7X^2+6X-3?

The degree of the polynomial 4X^3-7X^2+6X-3 is 3, as the highest exponent in the equation is 3.

How do I group like terms in a polynomial equation?

To group like terms in a polynomial equation, identify terms with the same variables and exponents, and combine them by adding or subtracting their coefficients.

What is the distributive property and how is it used in solving polynomial equations?

The distributive property states that when multiplying a number by a sum or difference, the result is the same as multiplying each addend or subtrahend by the number and then adding or subtracting the products. In solving polynomial equations, the distributive property is used to simplify the equation by breaking down larger terms into smaller, more manageable terms.

What are some common algebraic techniques used to solve polynomial equations?

Some common algebraic techniques used to solve polynomial equations include factoring, the quadratic formula, and completing the square. These techniques help to either break down the equation into simpler terms or find the roots of the equation.

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