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f(x)=(6x^2+3x+-2)/((x^2+5)(x^2+12))−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫6x2+3x−2(x2+5)(x2+12)dx\int\frac{6x^2+3x-2}{\left(x^2+5\right)\left(x^2+12\right)}dx

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Final answer to the exercise

−32arctan⁡(x5)75+37ln⁡∣x2+5∣+74arctan⁡(x12)712+37ln⁡∣12x2+12∣+C1\frac{-32\arctan\left(\frac{x}{\sqrt{5}}\right)}{7\sqrt{5}}+\frac{3}{7}\ln\left|\sqrt{x^2+5}\right|+\frac{74\arctan\left(\frac{x}{\sqrt{12}}\right)}{7\sqrt{12}}+\frac{3}{7}\ln\left|\frac{\sqrt{12}}{\sqrt{x^2+12}}\right|+C_1

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∫6x2+3x−2(x2+5)(x2+12) dx
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