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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 fraction $\frac{3x^3-x^2+4x+1}{\left(x^2+2\right)\left(x^2+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{2x-3}{x^2+2}+\frac{x+2}{x^2+1}$
Learn how to solve problems step by step online. Find the integral int((3x^3-x^24x+1)/((x^2+2)(x^2+1)))dx. Rewrite the fraction \frac{3x^3-x^2+4x+1}{\left(x^2+2\right)\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2x-3}{x^2+2}+\frac{x+2}{x^2+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2x-3}{x^2+2}dx results in: -2\ln\left(\frac{\sqrt{2}}{\sqrt{x^2+2}}\right)-3\cdot \left(\frac{1}{\sqrt{2}}\right)\arctan\left(\frac{x}{\sqrt{2}}\right). Gather the results of all integrals.
