Optimal. Leaf size=37 \[ -\frac {a^3}{3 x^3}-\frac {3 a^2 b}{2 x^2}-\frac {3 a b^2}{x}+b^3 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 37, 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*} -\frac {a^3}{3 x^3}-\frac {3 a^2 b}{2 x^2}-\frac {3 a b^2}{x}+b^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^4} \, dx &=\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\\ &=-\frac {a^3}{3 x^3}-\frac {3 a^2 b}{2 x^2}-\frac {3 a b^2}{x}+b^3 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} -\frac {a^3}{3 x^3}-\frac {3 a^2 b}{2 x^2}-\frac {3 a b^2}{x}+b^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 34, normalized size = 0.92
method | result | size |
default | \(-\frac {a^{3}}{3 x^{3}}-\frac {3 a^{2} b}{2 x^{2}}-\frac {3 a \,b^{2}}{x}+b^{3} \ln \left (x \right )\) | \(34\) |
norman | \(\frac {-\frac {1}{3} a^{3}-3 a \,b^{2} x^{2}-\frac {3}{2} a^{2} b x}{x^{3}}+b^{3} \ln \left (x \right )\) | \(34\) |
risch | \(\frac {-\frac {1}{3} a^{3}-3 a \,b^{2} x^{2}-\frac {3}{2} a^{2} b x}{x^{3}}+b^{3} \ln \left (x \right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 34, normalized size = 0.92 \begin {gather*} b^{3} \log \left (x\right ) - \frac {18 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3}}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.24, size = 37, normalized size = 1.00 \begin {gather*} \frac {6 \, b^{3} x^{3} \log \left (x\right ) - 18 \, a b^{2} x^{2} - 9 \, a^{2} b x - 2 \, a^{3}}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.07, size = 36, normalized size = 0.97 \begin {gather*} b^{3} \log {\left (x \right )} + \frac {- 2 a^{3} - 9 a^{2} b x - 18 a b^{2} x^{2}}{6 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.38, size = 35, normalized size = 0.95 \begin {gather*} b^{3} \log \left ({\left | x \right |}\right ) - \frac {18 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3}}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.07, size = 34, normalized size = 0.92 \begin {gather*} b^3\,\ln \left (x\right )-\frac {\frac {a^3}{3}+\frac {3\,a^2\,b\,x}{2}+3\,a\,b^2\,x^2}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________