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f(x)=(6x^2)/(x^4-5x^2+4)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫6x2x4−5x2+4dx\int\frac{6x^2}{x^4-5x^2+4}dx

Step-by-step Solution

Learn how to solve problems step by step online. Find the integral int((6x^2)/(x^4-5x^2+4))dx. Rewrite the expression \frac{6x^2}{x^4-5x^2+4} inside the integral in factored form. Take out the constant 6 from the integral. Rewrite the fraction \frac{x^2}{\left(x+1\right)\left(x+2\right)\left(x-2\right)\left(x-1\right)} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{6\left(x+1\right)}+\frac{-1}{3\left(x+2\right)}+\frac{1}{3\left(x-2\right)}+\frac{-1}{6\left(x-1\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral int((6x^2)/(x^4-5x^2+4))dx

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Final answer to the exercise

ln⁡∣x+1∣−2ln⁡∣x+2∣+2ln⁡∣x−2∣−ln⁡∣x−1∣+C0\ln\left|x+1\right|-2\ln\left|x+2\right|+2\ln\left|x-2\right|-\ln\left|x-1\right|+C_0

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  • Product of Binomials with Common Term
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∫6x2x4−5x2+4 dx
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