Optimal. Leaf size=17 \[ -\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \[ -\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^4} \, dx &=\int \left (\frac {a}{x^4}+\frac {b}{x^3}\right ) \, dx\\ &=-\frac {a}{3 x^3}-\frac {b}{2 x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {a}{3 x^3}-\frac {b}{2 x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.38, size = 13, normalized size = 0.76 \[ -\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.38, size = 13, normalized size = 0.76 \[ -\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ -\frac {b}{2 x^{2}}-\frac {a}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.10, size = 13, normalized size = 0.76 \[ -\frac {3 \, b x + 2 \, a}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 13, normalized size = 0.76 \[ -\frac {2\,a+3\,b\,x}{6\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 14, normalized size = 0.82 \[ \frac {- 2 a - 3 b x}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________