- #1
Denisse
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Homework Statement
How can I integrate this? I already tried substitution u=x-1 and partial fractions.
∫[dx]/[(1-X^2)√((x^2)-3x+2)]
The formula for integrating 1/(x-1)(sqrt(x^2-3x+2)) is ln|x-1| - 1/2sqrt(x^2-3x+2) + C, where C is the constant of integration.
Yes, this integral can be solved using the substitution u = x^2-3x+2. This will simplify the integral to 1/(u-1), which can be integrated using the formula mentioned above.
The steps for solving this integral are as follows:
1. Perform substitution u = x^2-3x+2
2. Rewrite the integral as 1/(u-1)
3. Use the formula for integrating 1/(u-1)
4. Substitute back u = x^2-3x+2 and simplify
5. Add the constant of integration C.
Yes, it is possible to solve this integral using partial fractions. However, it may be more complicated and time-consuming compared to using substitution.
Yes, this integral can also be solved using integration by parts. However, it may require multiple iterations of integration by parts and can be more complex compared to using substitution or partial fractions.