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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 $\frac{2x^3+2x^2+8}{\left(x^2-4x+4\right)\left(x^2+4\right)}$ inside the integral in factored form
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$\int\frac{2x^3+2x^2+8}{\left(x-2\right)^{2}\left(x^2+4\right)}dx$
Learn how to solve problems step by step online. Find the integral int((2x^3+2x^2+8)/((x^2-4x+4)(x^2+4)))dx. Rewrite the expression \frac{2x^3+2x^2+8}{\left(x^2-4x+4\right)\left(x^2+4\right)} inside the integral in factored form. Rewrite the fraction \frac{2x^3+2x^2+8}{\left(x-2\right)^{2}\left(x^2+4\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{4}{\left(x-2\right)^{2}}+\frac{2}{x^2+4}+\frac{2}{x-2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{4}{\left(x-2\right)^{2}}dx results in: \frac{-4}{x-2}.
