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

Exercise

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

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Final answer to the exercise

3x128(x2+4)+3256arctan⁡(x2)+x16(x2+4)2+−5256vv2+4−5512arctan⁡(v2)+−596v(v2+4)2+−v6(v2+4)3+C0\frac{3x}{128\left(x^{2}+4\right)}+\frac{3}{256}\arctan\left(\frac{x}{2}\right)+\frac{x}{16\left(x^{2}+4\right)^{2}}+\frac{-\frac{5}{256}v}{v^{2}+4}-\frac{5}{512}\arctan\left(\frac{v}{2}\right)+\frac{-\frac{5}{96}v}{\left(v^{2}+4\right)^{2}}+\frac{-v}{6\left(v^{2}+4\right)^{3}}+C_0

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∫x2(x2+4)4 dx
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