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

Exercise

∫x4+x3+1(x2+4)3dx\int\frac{x^4+x^3+1}{\left(x^2+4\right)^3}dx

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Final answer to the exercise

−xx2+4+1−2(x2+4)+51x128(x2+4)+51256arctan⁡(x2)+17x16(x2+4)2+1(x2+4)2+C0\frac{-x}{x^2+4}+\frac{1}{-2\left(x^2+4\right)}+\frac{51x}{128\left(x^2+4\right)}+\frac{51}{256}\arctan\left(\frac{x}{2}\right)+\frac{17x}{16\left(x^2+4\right)^{2}}+\frac{1}{\left(x^2+4\right)^{2}}+C_0

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∫x4+x3+1(x2+4)3 dx
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