Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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For each factor of the form \((px + q)^m\), the partial fraction decomposition must include the following sum of \(m\) fractions: \[ \frac{A_1}{px + q} + \frac{A_2}{(px + q)^2} + \frac{A_3}{(px + q)^3} + \cdots + \frac{A_m}{(px + q)^m} \] For each factor of the form \((ax^2 + bx + c)^n\), the partial fraction decomposition must include the following sum of \(m\) fractions: \[ \frac{B_1x + C_1}{ax^2 + bx + c} + \frac{B_2x + C_2}{(ax^2 + bx + c)^2} + \frac{B_3x + C_3}{(ax^2 + bx + c)^3} + \cdots + \frac{B_nx + C_n}{(ax^2 + bx + c)^n} \] **Example:** \[ \int \frac{x^3}{x^2 + 4x + 3} \, dx \]
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Transcribed Image Text:For each factor of the form \((px + q)^m\), the partial fraction decomposition must include the following sum of \(m\) fractions: \[ \frac{A_1}{px + q} + \frac{A_2}{(px + q)^2} + \frac{A_3}{(px + q)^3} + \cdots + \frac{A_m}{(px + q)^m} \] For each factor of the form \((ax^2 + bx + c)^n\), the partial fraction decomposition must include the following sum of \(m\) fractions: \[ \frac{B_1x + C_1}{ax^2 + bx + c} + \frac{B_2x + C_2}{(ax^2 + bx + c)^2} + \frac{B_3x + C_3}{(ax^2 + bx + c)^3} + \cdots + \frac{B_nx + C_n}{(ax^2 + bx + c)^n} \] **Example:** \[ \int \frac{x^3}{x^2 + 4x + 3} \, dx \]
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