Optimal. Leaf size=16 \[ \frac{2 (c+d x)^{7/2}}{7 d} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0014248, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{2 (c+d x)^{7/2}}{7 d} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int (c+d x)^{5/2} \, dx &=\frac{2 (c+d x)^{7/2}}{7 d}\\ \end{align*}
Mathematica [A] time = 0.006018, size = 16, normalized size = 1. \[ \frac{2 (c+d x)^{7/2}}{7 d} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*}{\frac{2}{7\,d} \left ( dx+c \right ) ^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.952011, size = 16, normalized size = 1. \begin{align*} \frac{2 \,{\left (d x + c\right )}^{\frac{7}{2}}}{7 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.73007, size = 85, normalized size = 5.31 \begin{align*} \frac{2 \,{\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )} \sqrt{d x + c}}{7 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.059051, size = 12, normalized size = 0.75 \begin{align*} \frac{2 \left (c + d x\right )^{\frac{7}{2}}}{7 d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.07311, size = 81, normalized size = 5.06 \begin{align*} \frac{2 \,{\left (15 \,{\left (d x + c\right )}^{\frac{7}{2}} - 42 \,{\left (d x + c\right )}^{\frac{5}{2}} c + 70 \,{\left (d x + c\right )}^{\frac{3}{2}} c^{2} + 14 \,{\left (3 \,{\left (d x + c\right )}^{\frac{5}{2}} - 5 \,{\left (d x + c\right )}^{\frac{3}{2}} c\right )} c\right )}}{105 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]