Optimal. Leaf size=16 \[ \frac {2 (a+b x)^{3/2}}{3 b} \]
[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} \[ \frac {2 (a+b x)^{3/2}}{3 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin {align*} \int \sqrt {a+b x} \, dx &=\frac {2 (a+b x)^{3/2}}{3 b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {2 (a+b x)^{3/2}}{3 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 12, normalized size = 0.75 \[ \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.97, size = 12, normalized size = 0.75 \[ \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 12, normalized size = 0.75 \[ \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 12, normalized size = 0.75 \[ \frac {2\,{\left (a+b\,x\right )}^{3/2}}{3\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 12, normalized size = 0.75 \[ \frac {2 \left (a + b x\right )^{\frac {3}{2}}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________