Step-by-step Solution

Integral of $\frac{1}{1-x^2}$ with respect to x

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Step-by-step explanation

Problem to solve:

$\int\frac{dx}{1-x^2}$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{1}{\left(1+x\right)\left(1-x\right)}dx$

Unlock this full step-by-step solution!

Learn how to solve integrals by partial fraction expansion problems step by step online. Integral of 1/(1-x^2) with respect to x. Factor the difference of squares 1-x^2 as the product of two conjugated binomials. Rewrite the fraction \frac{1}{\left(1+x\right)\left(1-x\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(1+x\right)\left(1-x\right). Multiplying polynomials.

Final Answer

$\frac{1}{2}\ln\left|x+1\right|-\frac{1}{2}\ln\left|-x+1\right|+C_0$

Problem Analysis