Final Answer
$30\ln\left(x\right)-30\ln\left(x+1\right)+\frac{-7}{x}+\frac{37}{x+1}+\frac{37}{2\left(x+1\right)^{2}}+C_0$
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Step-by-step Solution
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Find the integral
$\int\left(\frac{7}{x^2\left(x+1\right)}+\frac{37}{x\left(x+1\right)^3}\right)dx$
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$\int\left(\frac{7}{x^2\left(x+1\right)}+\frac{37}{x\left(x+1\right)^3}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of 7/(x^2(x+1))+37/(x(x+1)^3). Find the integral. Expand the integral \int\left(\frac{7}{x^2\left(x+1\right)}+\frac{37}{x\left(x+1\right)^3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{7}{x^2\left(x+1\right)}dx results in: \frac{-7}{x}+7\ln\left(x+1\right)-7\ln\left(x\right). Gather the results of all integrals.
Final Answer
$30\ln\left(x\right)-30\ln\left(x+1\right)+\frac{-7}{x}+\frac{37}{x+1}+\frac{37}{2\left(x+1\right)^{2}}+C_0$