Optimal. Leaf size=14 \[ -\frac{1}{7 d (c+d x)^7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0016125, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ -\frac{1}{7 d (c+d x)^7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^8} \, dx &=-\frac{1}{7 d (c+d x)^7}\\ \end{align*}
Mathematica [A] time = 0.0026768, size = 14, normalized size = 1. \[ -\frac{1}{7 d (c+d x)^7} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{7\,d \left ( dx+c \right ) ^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.961186, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{7 \,{\left (d x + c\right )}^{7} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.75918, size = 162, normalized size = 11.57 \begin{align*} -\frac{1}{7 \,{\left (d^{8} x^{7} + 7 \, c d^{7} x^{6} + 21 \, c^{2} d^{6} x^{5} + 35 \, c^{3} d^{5} x^{4} + 35 \, c^{4} d^{4} x^{3} + 21 \, c^{5} d^{3} x^{2} + 7 \, c^{6} d^{2} x + c^{7} d\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.609726, size = 85, normalized size = 6.07 \begin{align*} - \frac{1}{7 c^{7} d + 49 c^{6} d^{2} x + 147 c^{5} d^{3} x^{2} + 245 c^{4} d^{4} x^{3} + 245 c^{3} d^{5} x^{4} + 147 c^{2} d^{6} x^{5} + 49 c d^{7} x^{6} + 7 d^{8} x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06536, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{7 \,{\left (d x + c\right )}^{7} d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]