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f(x)=(64+x^2)^(-6)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫(64+x2)−6dx\int\left(64+x^2\right)^{-6}dx

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Final answer to the exercise

4⋅89x5⋅646(64+x2)5+634x646(64+x2)+634arctan⁡(x8)8646+672x646(64+x2)2+1720325x646(64+x2)3+94371845x646(64+x2)4+C0\frac{4\cdot 8^{9}x}{5\cdot 64^{6}\left(64+x^2\right)^{5}}+\frac{\frac{63}{4}x}{64^{6}\left(64+x^2\right)}+\frac{\frac{63}{4}\arctan\left(\frac{x}{8}\right)}{864^{6}}+\frac{672x}{64^{6}\left(64+x^2\right)^{2}}+\frac{\frac{172032}{5}x}{64^{6}\left(64+x^2\right)^{3}}+\frac{\frac{9437184}{5}x}{64^{6}\left(64+x^2\right)^{4}}+C_0

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Similar Questions Solved

dydx=tan⁡(x+y)\frac{dy}{dx}=\tan\left(x+y\right)

Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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