Optimal. Leaf size=37 \[ -\frac {(x+1)^{12}}{14 x^{14}}+\frac {(x+1)^{12}}{91 x^{13}}-\frac {(x+1)^{12}}{1092 x^{12}} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {27, 45, 37} \begin {gather*} -\frac {(x+1)^{12}}{1092 x^{12}}+\frac {(x+1)^{12}}{91 x^{13}}-\frac {(x+1)^{12}}{14 x^{14}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 37
Rule 45
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{15}} \, dx &=\int \frac {(1+x)^{11}}{x^{15}} \, dx\\ &=-\frac {(1+x)^{12}}{14 x^{14}}-\frac {1}{7} \int \frac {(1+x)^{11}}{x^{14}} \, dx\\ &=-\frac {(1+x)^{12}}{14 x^{14}}+\frac {(1+x)^{12}}{91 x^{13}}+\frac {1}{91} \int \frac {(1+x)^{11}}{x^{13}} \, dx\\ &=-\frac {(1+x)^{12}}{14 x^{14}}+\frac {(1+x)^{12}}{91 x^{13}}-\frac {(1+x)^{12}}{1092 x^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.00, size = 79, normalized size = 2.14 \begin {gather*} -\frac {1}{14 x^{14}}-\frac {11}{13 x^{13}}-\frac {55}{12 x^{12}}-\frac {15}{x^{11}}-\frac {33}{x^{10}}-\frac {154}{3 x^9}-\frac {231}{4 x^8}-\frac {330}{7 x^7}-\frac {55}{2 x^6}-\frac {11}{x^5}-\frac {11}{4 x^4}-\frac {1}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{15}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 60, normalized size = 1.62 \begin {gather*} -\frac {364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 60, normalized size = 1.62 \begin {gather*} -\frac {364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 62, normalized size = 1.68 \begin {gather*} -\frac {1}{3 x^{3}}-\frac {11}{4 x^{4}}-\frac {11}{x^{5}}-\frac {55}{2 x^{6}}-\frac {330}{7 x^{7}}-\frac {231}{4 x^{8}}-\frac {154}{3 x^{9}}-\frac {33}{x^{10}}-\frac {15}{x^{11}}-\frac {55}{12 x^{12}}-\frac {11}{13 x^{13}}-\frac {1}{14 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.48, size = 60, normalized size = 1.62 \begin {gather*} -\frac {364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.08, size = 60, normalized size = 1.62 \begin {gather*} -\frac {\frac {x^{11}}{3}+\frac {11\,x^{10}}{4}+11\,x^9+\frac {55\,x^8}{2}+\frac {330\,x^7}{7}+\frac {231\,x^6}{4}+\frac {154\,x^5}{3}+33\,x^4+15\,x^3+\frac {55\,x^2}{12}+\frac {11\,x}{13}+\frac {1}{14}}{x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.18, size = 61, normalized size = 1.65 \begin {gather*} \frac {- 364 x^{11} - 3003 x^{10} - 12012 x^{9} - 30030 x^{8} - 51480 x^{7} - 63063 x^{6} - 56056 x^{5} - 36036 x^{4} - 16380 x^{3} - 5005 x^{2} - 924 x - 78}{1092 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________