Optimal. Leaf size=24 \[ -\frac {a^2}{2 x^2}-\frac {2 a b}{x}+b^2 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 24, 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^2}{2 x^2}-\frac {2 a b}{x}+b^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^3} \, dx &=\int \left (\frac {a^2}{x^3}+\frac {2 a b}{x^2}+\frac {b^2}{x}\right ) \, dx\\ &=-\frac {a^2}{2 x^2}-\frac {2 a b}{x}+b^2 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 24, normalized size = 1.00 \begin {gather*} -\frac {a^2}{2 x^2}-\frac {2 a b}{x}+b^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 23, normalized size = 0.96
method | result | size |
default | \(-\frac {a^{2}}{2 x^{2}}-\frac {2 a b}{x}+b^{2} \ln \left (x \right )\) | \(23\) |
norman | \(\frac {-\frac {1}{2} a^{2}-2 a b x}{x^{2}}+b^{2} \ln \left (x \right )\) | \(23\) |
risch | \(\frac {-\frac {1}{2} a^{2}-2 a b x}{x^{2}}+b^{2} \ln \left (x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 21, normalized size = 0.88 \begin {gather*} b^{2} \log \left (x\right ) - \frac {4 \, a b x + a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.52, size = 26, normalized size = 1.08 \begin {gather*} \frac {2 \, b^{2} x^{2} \log \left (x\right ) - 4 \, a b x - a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 22, normalized size = 0.92 \begin {gather*} b^{2} \log {\left (x \right )} + \frac {- a^{2} - 4 a b x}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.37, size = 22, normalized size = 0.92 \begin {gather*} b^{2} \log \left ({\left | x \right |}\right ) - \frac {4 \, a b x + a^{2}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 23, normalized size = 0.96 \begin {gather*} b^2\,\ln \left (x\right )-\frac {\frac {a^2}{2}+2\,b\,x\,a}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________