Optimal. Leaf size=69 \[ -\frac {a^5}{27 x^{27}}-\frac {5 a^4 b}{24 x^{24}}-\frac {10 a^3 b^2}{21 x^{21}}-\frac {5 a^2 b^3}{9 x^{18}}-\frac {a b^4}{3 x^{15}}-\frac {b^5}{12 x^{12}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac {10 a^3 b^2}{21 x^{21}}-\frac {5 a^2 b^3}{9 x^{18}}-\frac {5 a^4 b}{24 x^{24}}-\frac {a^5}{27 x^{27}}-\frac {a b^4}{3 x^{15}}-\frac {b^5}{12 x^{12}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^{28}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^{10}} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {a^5}{x^{10}}+\frac {5 a^4 b}{x^9}+\frac {10 a^3 b^2}{x^8}+\frac {10 a^2 b^3}{x^7}+\frac {5 a b^4}{x^6}+\frac {b^5}{x^5}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5}{27 x^{27}}-\frac {5 a^4 b}{24 x^{24}}-\frac {10 a^3 b^2}{21 x^{21}}-\frac {5 a^2 b^3}{9 x^{18}}-\frac {a b^4}{3 x^{15}}-\frac {b^5}{12 x^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 69, normalized size = 1.00 \[ -\frac {a^5}{27 x^{27}}-\frac {5 a^4 b}{24 x^{24}}-\frac {10 a^3 b^2}{21 x^{21}}-\frac {5 a^2 b^3}{9 x^{18}}-\frac {a b^4}{3 x^{15}}-\frac {b^5}{12 x^{12}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.84, size = 59, normalized size = 0.86 \[ -\frac {126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 59, normalized size = 0.86 \[ -\frac {126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 58, normalized size = 0.84 \[ -\frac {b^{5}}{12 x^{12}}-\frac {a \,b^{4}}{3 x^{15}}-\frac {5 a^{2} b^{3}}{9 x^{18}}-\frac {10 a^{3} b^{2}}{21 x^{21}}-\frac {5 a^{4} b}{24 x^{24}}-\frac {a^{5}}{27 x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 59, normalized size = 0.86 \[ -\frac {126 \, b^{5} x^{15} + 504 \, a b^{4} x^{12} + 840 \, a^{2} b^{3} x^{9} + 720 \, a^{3} b^{2} x^{6} + 315 \, a^{4} b x^{3} + 56 \, a^{5}}{1512 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 59, normalized size = 0.86 \[ -\frac {\frac {a^5}{27}+\frac {5\,a^4\,b\,x^3}{24}+\frac {10\,a^3\,b^2\,x^6}{21}+\frac {5\,a^2\,b^3\,x^9}{9}+\frac {a\,b^4\,x^{12}}{3}+\frac {b^5\,x^{15}}{12}}{x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.79, size = 63, normalized size = 0.91 \[ \frac {- 56 a^{5} - 315 a^{4} b x^{3} - 720 a^{3} b^{2} x^{6} - 840 a^{2} b^{3} x^{9} - 504 a b^{4} x^{12} - 126 b^{5} x^{15}}{1512 x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________