Final Answer
$\frac{4}{y}+2\ln\left(y+2\right)+2\ln\left(y\right)+C_0$
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Step-by-step Solution
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1
Rewrite the expression $\frac{4y^2-8}{y^3+2y^2}$ inside the integral in factored form
$\int\frac{4y^2-8}{y^2\left(y+2\right)}dy$
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$\int\frac{4y^2-8}{y^2\left(y+2\right)}dy$
Learn how to solve problems step by step online. Find the integral int((4y^2-8)/(y^3+2y^2))dy. Rewrite the expression \frac{4y^2-8}{y^3+2y^2} inside the integral in factored form. Rewrite the fraction \frac{4y^2-8}{y^2\left(y+2\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by y^2\left(y+2\right). Multiplying polynomials.
Final Answer
$\frac{4}{y}+2\ln\left(y+2\right)+2\ln\left(y\right)+C_0$