Final answer to the problem
$\frac{5}{2}\ln\left|x+9\right|+\frac{5}{2}\ln\left|x-9\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the expression $\frac{5x}{x^2-81}$ inside the integral in factored form
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$\int\frac{5x}{\left(x+9\right)\left(x-9\right)}dx$
Learn how to solve problems step by step online. Find the integral int((5x)/(x^2-81))dx. Rewrite the expression \frac{5x}{x^2-81} inside the integral in factored form. Take out the constant 5 from the integral. Rewrite the fraction \frac{x}{\left(x+9\right)\left(x-9\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2\left(x+9\right)}+\frac{1}{2\left(x-9\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$\frac{5}{2}\ln\left|x+9\right|+\frac{5}{2}\ln\left|x-9\right|+C_0$
