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

Exercise

∫2x2+3x−1(x−2)(x2+x+4)dx\int\frac{2x^2+3x-1}{\left(x-2\right)\left(x^2+x+4\right)}dx

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Final answer to the exercise

1310ln⁡∣x−2∣+1115arctan⁡(1+2x15)30+710ln⁡∣(x+12)2+154∣+C2\frac{13}{10}\ln\left|x-2\right|+\frac{11\sqrt{15}\arctan\left(\frac{1+2x}{\sqrt{15}}\right)}{30}+\frac{7}{10}\ln\left|\sqrt{\left(x+\frac{1}{2}\right)^2+\frac{15}{4}}\right|+C_2

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∫2x2+3x−1(x−2)(x2+x+4) dx
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