Optimal. Leaf size=16 \[ \frac {2 (a+b x)^{5/2}}{5 b} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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}
\begin {gather*} \frac {2 (a+b x)^{5/2}}{5 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin {align*} \int (a+b x)^{3/2} \, dx &=\frac {2 (a+b x)^{5/2}}{5 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 (a+b x)^{5/2}}{5 b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 13, normalized size = 0.81
method | result | size |
gosper | \(\frac {2 \left (b x +a \right )^{\frac {5}{2}}}{5 b}\) | \(13\) |
derivativedivides | \(\frac {2 \left (b x +a \right )^{\frac {5}{2}}}{5 b}\) | \(13\) |
default | \(\frac {2 \left (b x +a \right )^{\frac {5}{2}}}{5 b}\) | \(13\) |
trager | \(\frac {2 \left (x^{2} b^{2}+2 a b x +a^{2}\right ) \sqrt {b x +a}}{5 b}\) | \(29\) |
risch | \(\frac {2 \left (x^{2} b^{2}+2 a b x +a^{2}\right ) \sqrt {b x +a}}{5 b}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \, {\left (b x + a\right )}^{\frac {5}{2}}}{5 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs.
\(2 (12) = 24\).
time = 0.41, size = 28, normalized size = 1.75 \begin {gather*} \frac {2 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \sqrt {b x + a}}{5 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \left (a + b x\right )^{\frac {5}{2}}}{5 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (12) = 24\).
time = 0.97, size = 58, normalized size = 3.62 \begin {gather*} \frac {2 \, {\left (3 \, {\left (b x + a\right )}^{\frac {5}{2}} - 10 \, {\left (b x + a\right )}^{\frac {3}{2}} a + 30 \, \sqrt {b x + a} a^{2} + 10 \, {\left ({\left (b x + a\right )}^{\frac {3}{2}} - 3 \, \sqrt {b x + a} a\right )} a\right )}}{15 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} \frac {2\,{\left (a+b\,x\right )}^{5/2}}{5\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________