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Rewrite the expression $\frac{4x^2+9}{\left(x^2-24x+144\right)\left(x^2+3x+4\right)}$ inside the integral in factored form
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$\int\frac{4x^2+9}{\left(x-12\right)^{2}\left(x^2+3x+4\right)}dx$
Learn how to solve problems step by step online. Find the integral int((4x^2+9)/((x^2-24x+144)(x^2+3x+4)))dx. Rewrite the expression \frac{4x^2+9}{\left(x^2-24x+144\right)\left(x^2+3x+4\right)} inside the integral in factored form. Rewrite the fraction \frac{4x^2+9}{\left(x-12\right)^{2}\left(x^2+3x+4\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{3.1793478}{\left(x-12\right)^{2}}+\frac{-\frac{26}{471}x-7.41\times 10^{-3}}{x^2+3x+4}+\frac{26}{471\left(x-12\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{3.1793478}{\left(x-12\right)^{2}}dx results in: \frac{-585.0006906}{184.0002172\left(x-12\right)}.
