Integration with Partial Fractions (Example 1)

✔ https://StudyForce.com ✔ https://Biology-Forums.com ✔ Ask questions here: https://Biology-Forums.com/index.php?... Follow us: ▶ Facebook:   / studyforceps   ▶ Instagram:   / studyforceonline   ▶ Twitter:   / studyforceps   The goal is to convert: 1)∫1▒〖(4x+5)/(x^2+x−2) → 2)∫1▒〖3/(x−1)+1/(x+2)〗〗 Because Equation 2 is a lot easier to integrate than Equation 1, yet they are the same! Recall: ∫1▒〖1/(x+n)=ln⁡〖|x+n|+c〗 where n is a constant〗 The technique used to convert a rational function as a sum of partial fractions of the form is summarized below: A/(ax+b)^i or (Ax+B)/(ax^2+bx+c)^j Note: This method only applies if the highest power in the numerator is less than the highest power in the denominator. Q. (Difficulty: Hard)