Final answer to the problem
$\frac{17}{x}+\ln\left|x-17\right|-\ln\left|x\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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1
Rewrite the expression $\frac{289}{x^3-17x^2}$ inside the integral in factored form
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$\int\frac{289}{x^2\left(x-17\right)}dx$
Learn how to solve problems step by step online. Find the integral int(289/(x^3-17x^2))dx. Rewrite the expression \frac{289}{x^3-17x^2} inside the integral in factored form. Rewrite the fraction \frac{289}{x^2\left(x-17\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-17}{x^2}+\frac{1}{x-17}+\frac{-1}{x}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-17}{x^2}dx results in: \frac{17}{x}.
Final answer to the problem
$\frac{17}{x}+\ln\left|x-17\right|-\ln\left|x\right|+C_0$
