Final answer to the problem
$\frac{1}{3}\ln\left|x\right|+\frac{2}{3}\ln\left|\sqrt{x^2-3}\right|+C_1$
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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 $\frac{x^2-1}{x^3-3x}$ inside the integral in factored form
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$\int\frac{x^2-1}{x\left(x^2-3\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^2-1)/(x^3-3x))dx. Rewrite the expression \frac{x^2-1}{x^3-3x} inside the integral in factored form. Rewrite the fraction \frac{x^2-1}{x\left(x^2-3\right)} in 2 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{1}{3x}dx results in: \frac{1}{3}\ln\left(x\right).
Final answer to the problem
$\frac{1}{3}\ln\left|x\right|+\frac{2}{3}\ln\left|\sqrt{x^2-3}\right|+C_1$
