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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((1+x^2)/(x^4+1))dx. Rewrite the expression \frac{1+x^2}{x^4+1} inside the integral in factored form. Rewrite the fraction \frac{1+x^2}{\left(x^2-\sqrt{2}x+1\right)\left(x^2+\sqrt{2}x+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-\sqrt{2}x+1\right)\left(x^2+\sqrt{2}x+1\right). Multiplying polynomials.
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.