# URGENT!!! Calculus problem

• Mar 11th 2009, 10:07 PM
Pikachu91
URGENT!!! Calculus problem
Please show all steps and all the work that is required for the problem.
∫ ( dx/ x^3+1) from 0 to 1.

1. Set up the appropriate partial fraction expression.
2. Determine the coefficients.
3. Develop completely the procedure for integration of each integral.
4. Apply the integration limits to obtain the final expression.

• Mar 11th 2009, 10:17 PM
Quote:

Originally Posted by Pikachu91
Please show all steps and all the work that is required for the problem.
∫ ( dx/ x^3+1) from 0 to 1.

1. Set up the appropriate partial fraction expression.
2. Determine the coefficients.
3. Develop completely the procedure for integration of each integral.
4. Apply the integration limits to obtain the final expression.

1)∫ ( dx/ x^3+1)
$\displaystyle \int { \frac{dx}{(x+1)(x^2 + x + 1)} }$

$\displaystyle \frac{1}{(x+1)(x^2 + x + 1)} = \frac{A}{(x+1)} + \frac{Bx+C}{(x^2 + x + 1)}$

Find value of A B and C that's 2 nd Part

3) You are expected to be able to find

$\displaystyle \int{ \frac{A}{(x+1)} + \frac{Bx+C}{(x^2 + x + 1)}}$

4) First put x=1 after integration and then deduce it from the value of integration for x= 1

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