Final Answer
$4\ln\left(x\right)-\frac{21\sqrt{2}}{4}\arctan\left(\frac{\sqrt{2}}{4}x\right)-\frac{1}{2}\ln\left(1+\left(\frac{\sqrt{2}}{4}x\right)^2\right)-3.63\times 10^{-6}x\arctan\left(\frac{\sqrt{2}}{4}x\right)+C_0$
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Step-by-step Solution
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We could not solve this problem by using the method: Integrate by parts
1
Combining like terms $-8x$ and $16x$
$\int\frac{3x^2-21x+32}{x^3+8x}dx$
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$\int\frac{3x^2-21x+32}{x^3+8x}dx$
Learn how to solve problems step by step online. Find the integral int((3x^2-21x+32)/(x^3-8x16x))dx. Combining like terms -8x and 16x. Rewrite the expression \frac{3x^2-21x+32}{x^3+8x} inside the integral in factored form. Rewrite the fraction \frac{3x^2-21x+32}{x\left(x^2+8\right)} in 2 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\left(x^2+8\right).
Final Answer
$4\ln\left(x\right)-\frac{21\sqrt{2}}{4}\arctan\left(\frac{\sqrt{2}}{4}x\right)-\frac{1}{2}\ln\left(1+\left(\frac{\sqrt{2}}{4}x\right)^2\right)-3.63\times 10^{-6}x\arctan\left(\frac{\sqrt{2}}{4}x\right)+C_0$