Final answer to the problem
$\frac{45}{8}\ln\left|\frac{8\left(x+\frac{3}{8}\right)}{5}-1\right|-\frac{45}{8}\ln\left|\frac{3+8x}{5}+1\right|-\frac{27}{8}\ln\left|8x-2\right|-\frac{27}{8}\ln\left|8x+8\right|+C_0$
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Step-by-step Solution
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1
Rewrite the expression $\frac{18-27x}{4x^2+3x-1}$ inside the integral in factored form
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$\int\frac{9\left(2-3x\right)}{4\left(\left(x+\frac{3}{8}\right)^2-\frac{1}{4}-\frac{9}{64}\right)}dx$
Learn how to solve problems step by step online. Find the integral int((18-27x)/(4x^2+3x+-1))dx. Rewrite the expression \frac{18-27x}{4x^2+3x-1} inside the integral in factored form. Take out the constant 9 from the integral. Take the constant \frac{1}{4} out of the integral. Multiply the fraction and term in 9\cdot \left(\frac{1}{4}\right)\int\frac{2-3x}{\left(x+\frac{3}{8}\right)^2-\frac{1}{4}-\frac{9}{64}}dx.
Final answer to the problem
$\frac{45}{8}\ln\left|\frac{8\left(x+\frac{3}{8}\right)}{5}-1\right|-\frac{45}{8}\ln\left|\frac{3+8x}{5}+1\right|-\frac{27}{8}\ln\left|8x-2\right|-\frac{27}{8}\ln\left|8x+8\right|+C_0$
