Optimal. Leaf size=23 \[ \frac{2 (d (a+b x)+c)^{3/2}}{3 b d} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0241309, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{2 (d (a+b x)+c)^{3/2}}{3 b d} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[c + d*(a + b*x)],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.14334, size = 17, normalized size = 0.74 \[ \frac{2 \left (c + d \left (a + b x\right )\right )^{\frac{3}{2}}}{3 b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c+d*(b*x+a))**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0158129, size = 23, normalized size = 1. \[ \frac{2 (d (a+b x)+c)^{3/2}}{3 b d} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[c + d*(a + b*x)],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 20, normalized size = 0.9 \[{\frac{2}{3\,db} \left ( bdx+ad+c \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c+d*(b*x+a))^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33501, size = 26, normalized size = 1.13 \[ \frac{2 \,{\left ({\left (b x + a\right )} d + c\right )}^{\frac{3}{2}}}{3 \, b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)*d + c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.197036, size = 26, normalized size = 1.13 \[ \frac{2 \,{\left (b d x + a d + c\right )}^{\frac{3}{2}}}{3 \, b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)*d + c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.956185, size = 82, normalized size = 3.57 \[ \begin{cases} \sqrt{c} x & \text{for}\: b = 0 \wedge d = 0 \\x \sqrt{a d + c} & \text{for}\: b = 0 \\\sqrt{c} x & \text{for}\: d = 0 \\\frac{2 a \sqrt{a d + b d x + c}}{3 b} + \frac{2 x \sqrt{a d + b d x + c}}{3} + \frac{2 c \sqrt{a d + b d x + c}}{3 b d} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c+d*(b*x+a))**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209776, size = 26, normalized size = 1.13 \[ \frac{2 \,{\left (b d x + a d + c\right )}^{\frac{3}{2}}}{3 \, b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)*d + c),x, algorithm="giac")
[Out]