Optimal. Leaf size=39 \[ -\frac {a^3}{x}-\frac {9 a^2 b}{2 x^{2/3}}-\frac {9 a b^2}{\sqrt [3]{x}}+b^3 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac {9 a^2 b}{2 x^{2/3}}-\frac {a^3}{x}-\frac {9 a b^2}{\sqrt [3]{x}}+b^3 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^3}{x^2} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^4} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {a^3}{x^4}+\frac {3 a^2 b}{x^3}+\frac {3 a b^2}{x^2}+\frac {b^3}{x}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^3}{x}-\frac {9 a^2 b}{2 x^{2/3}}-\frac {9 a b^2}{\sqrt [3]{x}}+b^3 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 39, normalized size = 1.00 \[ -\frac {a^3}{x}-\frac {9 a^2 b}{2 x^{2/3}}-\frac {9 a b^2}{\sqrt [3]{x}}+b^3 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 39, normalized size = 1.00 \[ \frac {6 \, b^{3} x \log \left (x^{\frac {1}{3}}\right ) - 18 \, a b^{2} x^{\frac {2}{3}} - 9 \, a^{2} b x^{\frac {1}{3}} - 2 \, a^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 37, normalized size = 0.95 \[ b^{3} \log \left ({\left | x \right |}\right ) - \frac {18 \, a b^{2} x^{\frac {2}{3}} + 9 \, a^{2} b x^{\frac {1}{3}} + 2 \, a^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 34, normalized size = 0.87 \[ b^{3} \ln \relax (x )-\frac {9 a \,b^{2}}{x^{\frac {1}{3}}}-\frac {9 a^{2} b}{2 x^{\frac {2}{3}}}-\frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.90, size = 36, normalized size = 0.92 \[ b^{3} \log \relax (x) - \frac {18 \, a b^{2} x^{\frac {2}{3}} + 9 \, a^{2} b x^{\frac {1}{3}} + 2 \, a^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 37, normalized size = 0.95 \[ 3\,b^3\,\ln \left (x^{1/3}\right )-\frac {a^3+\frac {9\,a^2\,b\,x^{1/3}}{2}+9\,a\,b^2\,x^{2/3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.65, size = 36, normalized size = 0.92 \[ - \frac {a^{3}}{x} - \frac {9 a^{2} b}{2 x^{\frac {2}{3}}} - \frac {9 a b^{2}}{\sqrt [3]{x}} + b^{3} \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________