Optimal. Leaf size=61 \[ -\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 61, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ -\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x-\frac {a^4 b}{x^5}-\frac {a^5}{8 x^8}+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^9} \, dx &=\int \left (10 a^2 b^3+\frac {a^5}{x^9}+\frac {5 a^4 b}{x^6}+\frac {10 a^3 b^2}{x^3}+5 a b^4 x^3+b^5 x^6\right ) \, dx\\ &=-\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 61, normalized size = 1.00 \[ -\frac {a^5}{8 x^8}-\frac {a^4 b}{x^5}-\frac {5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac {5}{4} a b^4 x^4+\frac {b^5 x^7}{7} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 59, normalized size = 0.97 \[ \frac {8 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 560 \, a^{2} b^{3} x^{9} - 280 \, a^{3} b^{2} x^{6} - 56 \, a^{4} b x^{3} - 7 \, a^{5}}{56 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 56, normalized size = 0.92 \[ \frac {1}{7} \, b^{5} x^{7} + \frac {5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac {40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 56, normalized size = 0.92 \[ \frac {b^{5} x^{7}}{7}+\frac {5 a \,b^{4} x^{4}}{4}+10 a^{2} b^{3} x -\frac {5 a^{3} b^{2}}{x^{2}}-\frac {a^{4} b}{x^{5}}-\frac {a^{5}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.35, size = 56, normalized size = 0.92 \[ \frac {1}{7} \, b^{5} x^{7} + \frac {5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac {40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 57, normalized size = 0.93 \[ \frac {b^5\,x^7}{7}-\frac {\frac {a^5}{8}+a^4\,b\,x^3+5\,a^3\,b^2\,x^6}{x^8}+10\,a^2\,b^3\,x+\frac {5\,a\,b^4\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.29, size = 61, normalized size = 1.00 \[ 10 a^{2} b^{3} x + \frac {5 a b^{4} x^{4}}{4} + \frac {b^{5} x^{7}}{7} + \frac {- a^{5} - 8 a^{4} b x^{3} - 40 a^{3} b^{2} x^{6}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________