Optimal. Leaf size=21 \[ -\frac {\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {270}
\begin {gather*} -\frac {\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^5}{x^3} \, dx &=-\frac {\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(67\) vs. \(2(21)=42\).
time = 0.02, size = 67, normalized size = 3.19 \begin {gather*} \frac {-a^5-6 a^4 b \sqrt [3]{x}-15 a^3 b^2 x^{2/3}-20 a^2 b^3 x-15 a b^4 x^{4/3}-6 b^5 x^{5/3}}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs.
\(2(17)=34\).
time = 0.20, size = 58, normalized size = 2.76
method | result | size |
derivativedivides | \(-\frac {15 a \,b^{4}}{2 x^{\frac {2}{3}}}-\frac {10 a^{2} b^{3}}{x}-\frac {3 a^{4} b}{x^{\frac {5}{3}}}-\frac {15 a^{3} b^{2}}{2 x^{\frac {4}{3}}}-\frac {a^{5}}{2 x^{2}}-\frac {3 b^{5}}{x^{\frac {1}{3}}}\) | \(58\) |
default | \(-\frac {15 a \,b^{4}}{2 x^{\frac {2}{3}}}-\frac {10 a^{2} b^{3}}{x}-\frac {3 a^{4} b}{x^{\frac {5}{3}}}-\frac {15 a^{3} b^{2}}{2 x^{\frac {4}{3}}}-\frac {a^{5}}{2 x^{2}}-\frac {3 b^{5}}{x^{\frac {1}{3}}}\) | \(58\) |
trager | \(\frac {\left (x -1\right ) \left (a^{3} x +20 b^{3} x +a^{3}\right ) a^{2}}{2 x^{2}}-\frac {3 \left (5 b^{3} x +2 a^{3}\right ) a b}{2 x^{\frac {5}{3}}}-\frac {3 \left (2 b^{3} x +5 a^{3}\right ) b^{2}}{2 x^{\frac {4}{3}}}\) | \(67\) |
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. 55 vs.
\(2 (17) = 34\).
time = 0.29, size = 55, normalized size = 2.62 \begin {gather*} -\frac {6 \, b^{5} x^{\frac {5}{3}} + 15 \, a b^{4} x^{\frac {4}{3}} + 20 \, a^{2} b^{3} x + 15 \, a^{3} b^{2} x^{\frac {2}{3}} + 6 \, a^{4} b x^{\frac {1}{3}} + a^{5}}{2 \, x^{2}} \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. 57 vs.
\(2 (17) = 34\).
time = 0.36, size = 57, normalized size = 2.71 \begin {gather*} -\frac {20 \, a^{2} b^{3} x + a^{5} + 3 \, {\left (2 \, b^{5} x + 5 \, a^{3} b^{2}\right )} x^{\frac {2}{3}} + 3 \, {\left (5 \, a b^{4} x + 2 \, a^{4} b\right )} x^{\frac {1}{3}}}{2 \, x^{2}} \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. 70 vs.
\(2 (17) = 34\).
time = 0.29, size = 70, normalized size = 3.33 \begin {gather*} - \frac {a^{5}}{2 x^{2}} - \frac {3 a^{4} b}{x^{\frac {5}{3}}} - \frac {15 a^{3} b^{2}}{2 x^{\frac {4}{3}}} - \frac {10 a^{2} b^{3}}{x} - \frac {15 a b^{4}}{2 x^{\frac {2}{3}}} - \frac {3 b^{5}}{\sqrt [3]{x}} \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. 55 vs.
\(2 (17) = 34\).
time = 1.62, size = 55, normalized size = 2.62 \begin {gather*} -\frac {6 \, b^{5} x^{\frac {5}{3}} + 15 \, a b^{4} x^{\frac {4}{3}} + 20 \, a^{2} b^{3} x + 15 \, a^{3} b^{2} x^{\frac {2}{3}} + 6 \, a^{4} b x^{\frac {1}{3}} + a^{5}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.12, size = 55, normalized size = 2.62 \begin {gather*} -\frac {a^5+6\,b^5\,x^{5/3}+20\,a^2\,b^3\,x+6\,a^4\,b\,x^{1/3}+15\,a\,b^4\,x^{4/3}+15\,a^3\,b^2\,x^{2/3}}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________