Final answer to the problem
$\frac{-x^2\left(5x+1\right)^2}{8\left(4x-1\right)^{2}}+\frac{3271}{64}\ln\left(4x-1\right)+\frac{-1611}{64\left(4x-1\right)}+\frac{415}{4}x+\frac{25}{4}x^2+C_0$
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Step-by-step Solution
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Find the integral
$\int\frac{x^2\left(5x+1\right)^2}{\left(4x-1\right)^3}dx$
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$\int\frac{x^2\left(5x+1\right)^2}{\left(4x-1\right)^3}dx$
Learn how to solve problems step by step online. Integrate the function (x^2(5x+1)^2)/((4x-1)^3). Find the integral. Rewrite the fraction \frac{x^2\left(5x+1\right)^2}{\left(4x-1\right)^3} inside the integral as the product of two functions: x^2\left(5x+1\right)^2\frac{1}{\left(4x-1\right)^3}. We can solve the integral \int x^2\left(5x+1\right)^2\frac{1}{\left(4x-1\right)^3}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.
Final answer to the problem
$\frac{-x^2\left(5x+1\right)^2}{8\left(4x-1\right)^{2}}+\frac{3271}{64}\ln\left(4x-1\right)+\frac{-1611}{64\left(4x-1\right)}+\frac{415}{4}x+\frac{25}{4}x^2+C_0$