Optimal. Leaf size=18 \[ -\frac {c^5 (a-b x)^6}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75}
\begin {gather*} -\frac {c^5 (a-b x)^6}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 75
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^5}{x^4} \, dx &=-\frac {c^5 (a-b x)^6}{3 x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(18)=36\).
time = 0.01, size = 63, normalized size = 3.50 \begin {gather*} c^5 \left (-\frac {a^6}{3 x^3}+\frac {2 a^5 b}{x^2}-\frac {5 a^4 b^2}{x}-5 a^2 b^4 x+2 a b^5 x^2-\frac {b^6 x^3}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs.
\(2(16)=32\).
time = 0.05, size = 60, normalized size = 3.33
method | result | size |
gosper | \(-\frac {c^{5} \left (b^{6} x^{6}-6 a \,b^{5} x^{5}+15 a^{2} b^{4} x^{4}+15 a^{4} b^{2} x^{2}-6 a^{5} b x +a^{6}\right )}{3 x^{3}}\) | \(58\) |
default | \(c^{5} \left (-\frac {b^{6} x^{3}}{3}+2 a \,b^{5} x^{2}-5 a^{2} b^{4} x -\frac {5 a^{4} b^{2}}{x}+\frac {2 a^{5} b}{x^{2}}-\frac {a^{6}}{3 x^{3}}\right )\) | \(60\) |
risch | \(-\frac {b^{6} c^{5} x^{3}}{3}+2 b^{5} c^{5} a \,x^{2}-5 b^{4} c^{5} a^{2} x +\frac {-5 a^{4} b^{2} c^{5} x^{2}+2 a^{5} b \,c^{5} x -\frac {1}{3} a^{6} c^{5}}{x^{3}}\) | \(74\) |
norman | \(\frac {-\frac {1}{3} a^{6} c^{5}-\frac {1}{3} b^{6} c^{5} x^{6}+2 a \,b^{5} c^{5} x^{5}-5 a^{2} b^{4} c^{5} x^{4}-5 a^{4} b^{2} c^{5} x^{2}+2 a^{5} b \,c^{5} x}{x^{3}}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (17) = 34\).
time = 0.30, size = 73, normalized size = 4.06 \begin {gather*} -\frac {1}{3} \, b^{6} c^{5} x^{3} + 2 \, a b^{5} c^{5} x^{2} - 5 \, a^{2} b^{4} c^{5} x - \frac {15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (17) = 34\).
time = 1.52, size = 73, normalized size = 4.06 \begin {gather*} -\frac {b^{6} c^{5} x^{6} - 6 \, a b^{5} c^{5} x^{5} + 15 \, a^{2} b^{4} c^{5} x^{4} + 15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 76 vs.
\(2 (15) = 30\).
time = 0.11, size = 76, normalized size = 4.22 \begin {gather*} - 5 a^{2} b^{4} c^{5} x + 2 a b^{5} c^{5} x^{2} - \frac {b^{6} c^{5} x^{3}}{3} - \frac {a^{6} c^{5} - 6 a^{5} b c^{5} x + 15 a^{4} b^{2} c^{5} x^{2}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (17) = 34\).
time = 1.14, size = 73, normalized size = 4.06 \begin {gather*} -\frac {1}{3} \, b^{6} c^{5} x^{3} + 2 \, a b^{5} c^{5} x^{2} - 5 \, a^{2} b^{4} c^{5} x - \frac {15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.06, size = 74, normalized size = 4.11 \begin {gather*} 2\,a\,b^5\,c^5\,x^2-\frac {b^6\,c^5\,x^3}{3}-5\,a^2\,b^4\,c^5\,x-\frac {\frac {a^6\,c^5}{3}-2\,a^5\,b\,c^5\,x+5\,a^4\,b^2\,c^5\,x^2}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________