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- Integrate by partial fractions
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Rewrite the fraction $\frac{1}{\left(x^2+\sqrt{2}+1\right)\left(x^2-\sqrt{2}+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{-169}{478\left(x^2+\sqrt{2}+1\right)}+\frac{0.3535534}{x^2-\sqrt{2}+1}$
Learn how to solve problems step by step online. Find the integral int(1/((x^2+2^(1/2)+1)(x^2-2^(1/2)+1)))dx. Rewrite the fraction \frac{1}{\left(x^2+\sqrt{2}+1\right)\left(x^2-\sqrt{2}+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-169}{478\left(x^2+\sqrt{2}+1\right)}+\frac{0.3535534}{x^2-\sqrt{2}+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-169}{478\left(x^2+\sqrt{2}+1\right)}dx results in: \frac{-169\arctan\left(\frac{x}{\sqrt{1+\sqrt{2}}}\right)}{478\sqrt{1+\sqrt{2}}}. The integral \int\frac{0.3535534}{x^2-\sqrt{2}+1}dx results in: \frac{0.3535534\arctan\left(\frac{x}{\sqrt{1-\sqrt{2}}}\right)}{\sqrt{1-\sqrt{2}}}.
