Optimal. Leaf size=30 \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{3 x^3}-\frac {b^2}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 30, 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} \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{3 x^3}-\frac {b^2}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^5} \, dx &=\int \left (\frac {a^2}{x^5}+\frac {2 a b}{x^4}+\frac {b^2}{x^3}\right ) \, dx\\ &=-\frac {a^2}{4 x^4}-\frac {2 a b}{3 x^3}-\frac {b^2}{2 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ -\frac {a^2}{4 x^4}-\frac {2 a b}{3 x^3}-\frac {b^2}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.45, size = 24, normalized size = 0.80 \[ -\frac {6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.12, size = 24, normalized size = 0.80 \[ -\frac {6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 25, normalized size = 0.83 \[ -\frac {b^{2}}{2 x^{2}}-\frac {2 a b}{3 x^{3}}-\frac {a^{2}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.34, size = 24, normalized size = 0.80 \[ -\frac {6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 24, normalized size = 0.80 \[ -\frac {\frac {a^2}{4}+\frac {2\,a\,b\,x}{3}+\frac {b^2\,x^2}{2}}{x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.19, size = 26, normalized size = 0.87 \[ \frac {- 3 a^{2} - 8 a b x - 6 b^{2} x^{2}}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________