Evaluate the integral: integral (dx)/(1-x2)

April 9, 2026Mathematics

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April 9, 2026

Answer

(1-x)(1+x)$.

Here are the step-by-step solutions for the first 10 questions.

Question 9

Evaluate the integral: $\int \frac{dx}{1-x^2}$ Step 1: Factor the denominator. The denominator is a difference of squares: $1-x^2 = (1-x)(1+x)$ . Step 2: Perform partial fraction decomposition. Let $\frac{1}{(1-x)(1+x)} = \frac{A}{1-x} + \frac{B}{1+x}$ . Multiply by $(1-x)(1+x)$ : $1 = A(1+x) + B(1-x)$ Set $x=1$ : $1 = A(1

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Here are the step-by-step solutions for the first 10 questions.
Question 9 Evaluate the integral: (dx)/(1-x^2) Step 1: Factor the denominator.
The denominator is a difference of squares: 1-x^2 = (1-x)(1+x).
Let (1)/((1-x)(1+x)) = (A)/(1-x) + (B)/(1+x).

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

Here are the step-by-step solutions for the first 10 questions. Question 9 Evaluate the integral: (dx)/(1-x^2) Step 1: Factor the denominator. The denominator is a difference of squares: 1-x^2 = (1-x)(1+x). Step 2: Perform partial fraction decomposition. Let (1)/((1-x)(1+x)) = (A)/(1-x) + (B)/(1+x). Multiply by (1-x)(1+x): 1 = A(1+x) + B(1-x) Set x=1: $1 = A(1