Final answer to the problem
$\frac{-\left(x+3\right)^9}{33\left(3x-6\right)^{11}}+\frac{-78125}{22\left(3x-6\right)^{10}}+\frac{2104.3771044}{\left(3x-6\right)^{9}}+\frac{-552.3989899}{\left(3x-6\right)^{8}}+\frac{-84.1750842}{\left(3x-6\right)^{7}}+\frac{-8.1836887}{\left(3x-6\right)^{6}}+\frac{-0.5237561}{\left(3x-6\right)^{5}}+\frac{-\frac{6}{275}}{\left(3x-6\right)^{4}}+\frac{-\frac{1}{1804}}{\left(3x-6\right)^{3}}+\frac{-6.93\times 10^{-6}}{\left(3x-6\right)^{2}}+C_0$
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Step-by-step Solution
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Find the integral
$\int\frac{\left(x+3\right)^9}{\left(3x-6\right)^{12}}dx$
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$\int\frac{\left(x+3\right)^9}{\left(3x-6\right)^{12}}dx$
Learn how to solve problems step by step online. Integrate the function ((x+3)^9)/((3x-6)^12). Find the integral. Rewrite the fraction \frac{\left(x+3\right)^9}{\left(3x-6\right)^{12}} inside the integral as the product of two functions: \left(x+3\right)^9\frac{1}{\left(3x-6\right)^{12}}. We can solve the integral \int\left(x+3\right)^9\frac{1}{\left(3x-6\right)^{12}}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
$\frac{-\left(x+3\right)^9}{33\left(3x-6\right)^{11}}+\frac{-78125}{22\left(3x-6\right)^{10}}+\frac{2104.3771044}{\left(3x-6\right)^{9}}+\frac{-552.3989899}{\left(3x-6\right)^{8}}+\frac{-84.1750842}{\left(3x-6\right)^{7}}+\frac{-8.1836887}{\left(3x-6\right)^{6}}+\frac{-0.5237561}{\left(3x-6\right)^{5}}+\frac{-\frac{6}{275}}{\left(3x-6\right)^{4}}+\frac{-\frac{1}{1804}}{\left(3x-6\right)^{3}}+\frac{-6.93\times 10^{-6}}{\left(3x-6\right)^{2}}+C_0$