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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
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- Integrate using basic integrals
- Product of Binomials with Common Term
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Rewrite the expression $\frac{3x^3-x+1}{\left(x^2-x-7\right)\left(x^2+2x-3\right)}$ inside the integral in factored form
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$\int\frac{3x^3-x+1}{\left(x^2-x-7\right)\left(x-1\right)\left(x+3\right)}dx$
Learn how to solve problems step by step online. Find the integral int((3x^3-x+1)/((x^2-x+-7)(x^2+2x+-3)))dx. Rewrite the expression \frac{3x^3-x+1}{\left(x^2-x-7\right)\left(x^2+2x-3\right)} inside the integral in factored form. Rewrite the fraction \frac{3x^3-x+1}{\left(x^2-x-7\right)\left(x-1\right)\left(x+3\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{26}{35}x+\frac{47}{5}}{x^2-x-7}+\frac{-3}{28\left(x-1\right)}+\frac{77}{20\left(x+3\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-3}{28\left(x-1\right)}dx results in: -\frac{3}{28}\ln\left(x-1\right).
