Final answer to the problem
The integral diverges.
Step-by-step Solution
Specify the solving method
1
Factor the difference of squares $x^4-1$ as the product of two conjugated binomials
$\int\frac{1}{\left(x^{2}+1\right)\left(x^{2}-1\right)}dx$
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$\int\frac{1}{\left(x^{2}+1\right)\left(x^{2}-1\right)}dx$
Learn how to solve problems step by step online. Integrate the function 1/(x^4-1) from 0 to infinity. Factor the difference of squares x^4-1 as the product of two conjugated binomials. Rewrite the fraction \frac{1}{\left(x^{2}+1\right)\left(x^{2}-1\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(x^{2}+1\right)\left(x^{2}-1\right). Multiplying polynomials.
Final answer to the problem
The integral diverges.