Final Answer
$\frac{3}{2}\ln\left(y-1\right)-\ln\left(y\right)-\frac{3}{2}\ln\left(y+1\right)+\ln\left(y^2-1\right)+y+C_1$
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Step-by-step Solution
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1
Find the integral
$\int\left(\frac{1}{y^2-y}+\frac{2y+1}{y^2-1}+\frac{y}{y+1}\right)dy$
Learn how to solve trigonometric integrals problems step by step online.
$\int\left(\frac{1}{y^2-y}+\frac{2y+1}{y^2-1}+\frac{y}{y+1}\right)dy$
Learn how to solve trigonometric integrals problems step by step online. Find the integral of 1/(y^2-y)+(2y+1)/(y^2-1)y/(y+1). Find the integral. Expand the integral \int\left(\frac{1}{y^2-y}+\frac{2y+1}{y^2-1}+\frac{y}{y+1}\right)dy into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2y+1}{y^2-1}dy results in: \ln\left(y^2-1\right)-\frac{1}{2}\ln\left(y+1\right)+\frac{1}{2}\ln\left(y-1\right). Gather the results of all integrals.
Final Answer
$\frac{3}{2}\ln\left(y-1\right)-\ln\left(y\right)-\frac{3}{2}\ln\left(y+1\right)+\ln\left(y^2-1\right)+y+C_1$