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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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Factor the difference of squares $y^2-2$ as the product of two conjugated binomials
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$\int\frac{1}{\left(y+\sqrt{2}\right)\left(y-\sqrt{2}\right)}dy$
Learn how to solve problems step by step online. Find the integral int(1/(y^2-2))dy. Factor the difference of squares y^2-2 as the product of two conjugated binomials. Rewrite the fraction \frac{1}{\left(y+\sqrt{2}\right)\left(y-\sqrt{2}\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-169}{478\left(y+\sqrt{2}\right)}+\frac{0.3535534}{y-\sqrt{2}}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-169}{478\left(y+\sqrt{2}\right)}dy results in: -\frac{169}{478}\ln\left(y+\sqrt{2}\right).
