Optimal. Leaf size=35 \[ a^3 \log (x)+3 a^2 b x+\frac {3}{2} a b^2 x^2+\frac {b^3 x^3}{3} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 35, 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 = {43} \begin {gather*} 3 a^2 b x+a^3 \log (x)+\frac {3}{2} a b^2 x^2+\frac {b^3 x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x} \, dx &=\int \left (3 a^2 b+\frac {a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx\\ &=3 a^2 b x+\frac {3}{2} a b^2 x^2+\frac {b^3 x^3}{3}+a^3 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 35, normalized size = 1.00 \begin {gather*} a^3 \log (x)+3 a^2 b x+\frac {3}{2} a b^2 x^2+\frac {b^3 x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^3}{x} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.33, size = 31, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, b^{3} x^{3} + \frac {3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.95, size = 32, normalized size = 0.91 \begin {gather*} \frac {1}{3} \, b^{3} x^{3} + \frac {3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 32, normalized size = 0.91 \begin {gather*} \frac {b^{3} x^{3}}{3}+\frac {3 a \,b^{2} x^{2}}{2}+a^{3} \ln \relax (x )+3 a^{2} b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 31, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, b^{3} x^{3} + \frac {3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 31, normalized size = 0.89 \begin {gather*} a^3\,\ln \relax (x)+\frac {b^3\,x^3}{3}+\frac {3\,a\,b^2\,x^2}{2}+3\,a^2\,b\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 34, normalized size = 0.97 \begin {gather*} a^{3} \log {\relax (x )} + 3 a^{2} b x + \frac {3 a b^{2} x^{2}}{2} + \frac {b^{3} x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________