Optimal. Leaf size=17 \[ -\frac {a}{4 x^4}-\frac {b}{3 x^3} \]
________________________________________________________________________________________
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} \begin {gather*} -\frac {a}{4 x^4}-\frac {b}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^5} \, dx &=\int \left (\frac {a}{x^5}+\frac {b}{x^4}\right ) \, dx\\ &=-\frac {a}{4 x^4}-\frac {b}{3 x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {a}{4 x^4}-\frac {b}{3 x^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}{x^5} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.47, size = 13, normalized size = 0.76 \begin {gather*} -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.68, size = 13, normalized size = 0.76 \begin {gather*} -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} -\frac {b}{3 x^{3}}-\frac {a}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.05, size = 13, normalized size = 0.76 \begin {gather*} -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3\,a+4\,b\,x}{12\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.16, size = 14, normalized size = 0.82 \begin {gather*} \frac {- 3 a - 4 b x}{12 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________