Final Answer
$\frac{-1}{2\left(x+1\right)^{2}}+\frac{2}{x+1}+\ln\left(x+1\right)+\frac{5}{2\left(1+x\right)^{2}}+C_0$
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Step-by-step Solution
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1
Multiplying polynomials $\left(1+x\right)^{-3}$ and $x^2-5$
$\int\left(\left(1+x\right)^{-3}x^2-5\left(1+x\right)^{-3}\right)dx$
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$\int\left(\left(1+x\right)^{-3}x^2-5\left(1+x\right)^{-3}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int((x^2-5)(1+x)^(-3))dx. Multiplying polynomials \left(1+x\right)^{-3} and x^2-5. Expand the integral \int\left(\left(1+x\right)^{-3}x^2-5\left(1+x\right)^{-3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\left(1+x\right)^{-3}x^2dx results in: \ln\left(x+1\right)+\frac{2}{x+1}+\frac{-1}{2\left(x+1\right)^{2}}. Gather the results of all integrals.
Final Answer
$\frac{-1}{2\left(x+1\right)^{2}}+\frac{2}{x+1}+\ln\left(x+1\right)+\frac{5}{2\left(1+x\right)^{2}}+C_0$