Optimal. Leaf size=72 \[ \frac{x^5}{5}+\frac{11 x^4}{4}+\frac{55 x^3}{3}+\frac{165 x^2}{2}-\frac{165}{x^2}-\frac{55}{x^3}-\frac{55}{4 x^4}-\frac{11}{5 x^5}-\frac{1}{6 x^6}+330 x-\frac{462}{x}+462 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0216001, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {27, 43} \[ \frac{x^5}{5}+\frac{11 x^4}{4}+\frac{55 x^3}{3}+\frac{165 x^2}{2}-\frac{165}{x^2}-\frac{55}{x^3}-\frac{55}{4 x^4}-\frac{11}{5 x^5}-\frac{1}{6 x^6}+330 x-\frac{462}{x}+462 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 43
Rubi steps
\begin{align*} \int \frac{(1+x) \left (1+2 x+x^2\right )^5}{x^7} \, dx &=\int \frac{(1+x)^{11}}{x^7} \, dx\\ &=\int \left (330+\frac{1}{x^7}+\frac{11}{x^6}+\frac{55}{x^5}+\frac{165}{x^4}+\frac{330}{x^3}+\frac{462}{x^2}+\frac{462}{x}+165 x+55 x^2+11 x^3+x^4\right ) \, dx\\ &=-\frac{1}{6 x^6}-\frac{11}{5 x^5}-\frac{55}{4 x^4}-\frac{55}{x^3}-\frac{165}{x^2}-\frac{462}{x}+330 x+\frac{165 x^2}{2}+\frac{55 x^3}{3}+\frac{11 x^4}{4}+\frac{x^5}{5}+462 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0025686, size = 72, normalized size = 1. \[ \frac{x^5}{5}+\frac{11 x^4}{4}+\frac{55 x^3}{3}+\frac{165 x^2}{2}-\frac{165}{x^2}-\frac{55}{x^3}-\frac{55}{4 x^4}-\frac{11}{5 x^5}-\frac{1}{6 x^6}+330 x-\frac{462}{x}+462 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 59, normalized size = 0.8 \begin{align*} -{\frac{1}{6\,{x}^{6}}}-{\frac{11}{5\,{x}^{5}}}-{\frac{55}{4\,{x}^{4}}}-55\,{x}^{-3}-165\,{x}^{-2}-462\,{x}^{-1}+330\,x+{\frac{165\,{x}^{2}}{2}}+{\frac{55\,{x}^{3}}{3}}+{\frac{11\,{x}^{4}}{4}}+{\frac{{x}^{5}}{5}}+462\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0546, size = 78, normalized size = 1.08 \begin{align*} \frac{1}{5} \, x^{5} + \frac{11}{4} \, x^{4} + \frac{55}{3} \, x^{3} + \frac{165}{2} \, x^{2} + 330 \, x - \frac{27720 \, x^{5} + 9900 \, x^{4} + 3300 \, x^{3} + 825 \, x^{2} + 132 \, x + 10}{60 \, x^{6}} + 462 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.49849, size = 190, normalized size = 2.64 \begin{align*} \frac{12 \, x^{11} + 165 \, x^{10} + 1100 \, x^{9} + 4950 \, x^{8} + 19800 \, x^{7} + 27720 \, x^{6} \log \left (x\right ) - 27720 \, x^{5} - 9900 \, x^{4} - 3300 \, x^{3} - 825 \, x^{2} - 132 \, x - 10}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.131346, size = 63, normalized size = 0.88 \begin{align*} \frac{x^{5}}{5} + \frac{11 x^{4}}{4} + \frac{55 x^{3}}{3} + \frac{165 x^{2}}{2} + 330 x + 462 \log{\left (x \right )} - \frac{27720 x^{5} + 9900 x^{4} + 3300 x^{3} + 825 x^{2} + 132 x + 10}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.1258, size = 80, normalized size = 1.11 \begin{align*} \frac{1}{5} \, x^{5} + \frac{11}{4} \, x^{4} + \frac{55}{3} \, x^{3} + \frac{165}{2} \, x^{2} + 330 \, x - \frac{27720 \, x^{5} + 9900 \, x^{4} + 3300 \, x^{3} + 825 \, x^{2} + 132 \, x + 10}{60 \, x^{6}} + 462 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]