Optimal. Leaf size=19 \[ -\frac {3 a}{2 x^{2/3}}+3 b \sqrt [3]{x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} 3 b \sqrt [3]{x}-\frac {3 a}{2 x^{2/3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{5/3}} \, dx &=\int \left (\frac {a}{x^{5/3}}+\frac {b}{x^{2/3}}\right ) \, dx\\ &=-\frac {3 a}{2 x^{2/3}}+3 b \sqrt [3]{x}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} -\frac {3 (a-2 b x)}{2 x^{2/3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 14, normalized size = 0.74
method | result | size |
gosper | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
trager | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
risch | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
derivativedivides | \(-\frac {3 a}{2 x^{\frac {2}{3}}}+3 b \,x^{\frac {1}{3}}\) | \(14\) |
default | \(-\frac {3 a}{2 x^{\frac {2}{3}}}+3 b \,x^{\frac {1}{3}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 13, normalized size = 0.68 \begin {gather*} 3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.79, size = 13, normalized size = 0.68 \begin {gather*} \frac {3 \, {\left (2 \, b x - a\right )}}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.17, size = 17, normalized size = 0.89 \begin {gather*} - \frac {3 a}{2 x^{\frac {2}{3}}} + 3 b \sqrt [3]{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.17, size = 13, normalized size = 0.68 \begin {gather*} 3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} -\frac {3\,a-6\,b\,x}{2\,x^{2/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________