Integration by Splitting the Numerator

In this section we learn how to deal with a couple of special cases, in which the integrand is the quotient of two polynomials

Algebraic Division of Polynomials

As soon as the degree of the polynomial on the numerator is greater than, or equal to the degree of the polynomial on the denominator then this method is worth a try.


Exercise 1

Find each of the following integrals:

  1. \(\int \frac{x^2+1}{x+1}dx\)

  2. \(\int \frac{3x^2 + 4x - 3}{x+3}dx\)

  3. \(\int \frac{2x-1}{x+1}dx\)

  4. \(\int \frac{x^3 - x + 1}{x+2} dx\)

  5. \( \int \frac{4x^2+6x - 10}{2x^2+1}dx\)

    Note: this question is quite challenging.

Answers Without Working