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Exercise

$\int\frac{y^{2}-1}{y^{3}+y}dy$

Step-by-step Solution

Learn how to solve problems step by step online. Find the integral int((y^2-1)/(y^3+y))dy. Rewrite the expression \frac{y^2-1}{y^3+y} inside the integral in factored form. Rewrite the fraction \frac{y^2-1}{y\left(y^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{-1}{y}dy results in: -\ln\left(y\right).
Find the integral int((y^2-1)/(y^3+y))dy

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Final answer to the exercise

$-\ln\left|y\right|+\ln\left|y^2+1\right|+C_0$

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  • Product of Binomials with Common Term
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