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

Exercise

∫4x(x2+2)(x2+2x+3)dx\int\frac{4x}{\left(x^2+2\right)\left(x^2+2x+3\right)}dx

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Final answer to the exercise

16arctan⁡(x2)−20arctan⁡(x+12)92+49ln⁡∣x2+2∣+49ln⁡∣2(x+1)2+2∣+C1\frac{16\arctan\left(\frac{x}{\sqrt{2}}\right)-20\arctan\left(\frac{x+1}{\sqrt{2}}\right)}{9\sqrt{2}}+\frac{4}{9}\ln\left|\sqrt{x^2+2}\right|+\frac{4}{9}\ln\left|\frac{\sqrt{2}}{\sqrt{\left(x+1\right)^2+2}}\right|+C_1

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3.1083.10^8
∫4x(x2+2)(x2+2x+3) dx
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