Final answer to the problem
$\frac{-\left(x+4\right)^9}{28\left(4x-12\right)^{7}}+\frac{77207.15625}{\left(4x-12\right)^{6}}+\frac{26471.025}{\left(4x-12\right)^{5}}+\frac{4136.0976562}{\left(4x-12\right)^{4}}+\frac{-393.9140625}{\left(4x-12\right)^{3}}+\frac{-26.3781738}{\left(4x-12\right)^{2}}+\frac{-1.5073242}{4x-12}+\frac{7}{260}\ln\left(4x-12\right)+\frac{1}{3640}\left(4x-12\right)+6.13\times 10^{-7}\left(4x-12\right)^2+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\frac{\left(x+4\right)^9}{\left(4x-12\right)^8}dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\frac{\left(x+4\right)^9}{\left(4x-12\right)^8}dx$
Learn how to solve integrals of rational functions problems step by step online. Integrate the function ((x+4)^9)/((4x-12)^8). Find the integral. Rewrite the fraction \frac{\left(x+4\right)^9}{\left(4x-12\right)^8} inside the integral as the product of two functions: \left(x+4\right)^9\frac{1}{\left(4x-12\right)^8}. We can solve the integral \int\left(x+4\right)^9\frac{1}{\left(4x-12\right)^8}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
$\frac{-\left(x+4\right)^9}{28\left(4x-12\right)^{7}}+\frac{77207.15625}{\left(4x-12\right)^{6}}+\frac{26471.025}{\left(4x-12\right)^{5}}+\frac{4136.0976562}{\left(4x-12\right)^{4}}+\frac{-393.9140625}{\left(4x-12\right)^{3}}+\frac{-26.3781738}{\left(4x-12\right)^{2}}+\frac{-1.5073242}{4x-12}+\frac{7}{260}\ln\left(4x-12\right)+\frac{1}{3640}\left(4x-12\right)+6.13\times 10^{-7}\left(4x-12\right)^2+C_0$