Optimal. Leaf size=55 \[ -\frac {a^4 c^3}{7 x^7}+\frac {a^3 b c^3}{3 x^6}-\frac {a b^3 c^3}{2 x^4}+\frac {b^4 c^3}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75} \[ \frac {a^3 b c^3}{3 x^6}-\frac {a^4 c^3}{7 x^7}-\frac {a b^3 c^3}{2 x^4}+\frac {b^4 c^3}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 75
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^3}{x^8} \, dx &=\int \left (\frac {a^4 c^3}{x^8}-\frac {2 a^3 b c^3}{x^7}+\frac {2 a b^3 c^3}{x^5}-\frac {b^4 c^3}{x^4}\right ) \, dx\\ &=-\frac {a^4 c^3}{7 x^7}+\frac {a^3 b c^3}{3 x^6}-\frac {a b^3 c^3}{2 x^4}+\frac {b^4 c^3}{3 x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 47, normalized size = 0.85 \[ c^3 \left (-\frac {a^4}{7 x^7}+\frac {a^3 b}{3 x^6}-\frac {a b^3}{2 x^4}+\frac {b^4}{3 x^3}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 47, normalized size = 0.85 \[ \frac {14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.01, size = 47, normalized size = 0.85 \[ \frac {14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 40, normalized size = 0.73 \[ \left (\frac {b^{4}}{3 x^{3}}-\frac {a \,b^{3}}{2 x^{4}}+\frac {a^{3} b}{3 x^{6}}-\frac {a^{4}}{7 x^{7}}\right ) c^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.09, size = 47, normalized size = 0.85 \[ \frac {14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.29, size = 47, normalized size = 0.85 \[ -\frac {\frac {a^4\,c^3}{7}-\frac {a^3\,b\,c^3\,x}{3}+\frac {a\,b^3\,c^3\,x^3}{2}-\frac {b^4\,c^3\,x^4}{3}}{x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.33, size = 51, normalized size = 0.93 \[ - \frac {6 a^{4} c^{3} - 14 a^{3} b c^{3} x + 21 a b^{3} c^{3} x^{3} - 14 b^{4} c^{3} x^{4}}{42 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________