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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 problems step by step online. Integrate the function 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. Rewrite the fraction \frac{7}{x^2\left(x+1\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 x^2\left(x+1\right).