Optimal. Leaf size=14 \[ \frac{(c+d x)^{11}}{11 d} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0017762, 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} \[ \frac{(c+d x)^{11}}{11 d} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int (c+d x)^{10} \, dx &=\frac{(c+d x)^{11}}{11 d}\\ \end{align*}
Mathematica [A] time = 0.0010003, size = 14, normalized size = 1. \[ \frac{(c+d x)^{11}}{11 d} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( dx+c \right ) ^{11}}{11\,d}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.957012, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{11}}{11 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.59102, size = 230, normalized size = 16.43 \begin{align*} \frac{1}{11} x^{11} d^{10} + x^{10} d^{9} c + 5 x^{9} d^{8} c^{2} + 15 x^{8} d^{7} c^{3} + 30 x^{7} d^{6} c^{4} + 42 x^{6} d^{5} c^{5} + 42 x^{5} d^{4} c^{6} + 30 x^{4} d^{3} c^{7} + 15 x^{3} d^{2} c^{8} + 5 x^{2} d c^{9} + x c^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.077456, size = 114, normalized size = 8.14 \begin{align*} c^{10} x + 5 c^{9} d x^{2} + 15 c^{8} d^{2} x^{3} + 30 c^{7} d^{3} x^{4} + 42 c^{6} d^{4} x^{5} + 42 c^{5} d^{5} x^{6} + 30 c^{4} d^{6} x^{7} + 15 c^{3} d^{7} x^{8} + 5 c^{2} d^{8} x^{9} + c d^{9} x^{10} + \frac{d^{10} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06738, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{11}}{11 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]