Optimal. Leaf size=38 \[ \frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0646625, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{b (c+d x)^4}{4 d^2}-\frac{(c+d x)^3 (b c-a d)}{3 d^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(c + d*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.38052, size = 31, normalized size = 0.82 \[ \frac{b \left (c + d x\right )^{4}}{4 d^{2}} + \frac{\left (c + d x\right )^{3} \left (a d - b c\right )}{3 d^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(d*x+c)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0157489, size = 47, normalized size = 1.24 \[ \frac{1}{12} x \left (4 d x^2 (a d+2 b c)+6 c x (2 a d+b c)+12 a c^2+3 b d^2 x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(c + d*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 49, normalized size = 1.3 \[{\frac{b{d}^{2}{x}^{4}}{4}}+{\frac{ \left ( a{d}^{2}+2\,bcd \right ){x}^{3}}{3}}+{\frac{ \left ( 2\,acd+b{c}^{2} \right ){x}^{2}}{2}}+a{c}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(d*x+c)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.37426, size = 65, normalized size = 1.71 \[ \frac{1}{4} \, b d^{2} x^{4} + a c^{2} x + \frac{1}{3} \,{\left (2 \, b c d + a d^{2}\right )} x^{3} + \frac{1}{2} \,{\left (b c^{2} + 2 \, a c d\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.179914, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} d^{2} b + \frac{2}{3} x^{3} d c b + \frac{1}{3} x^{3} d^{2} a + \frac{1}{2} x^{2} c^{2} b + x^{2} d c a + x c^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.09534, size = 49, normalized size = 1.29 \[ a c^{2} x + \frac{b d^{2} x^{4}}{4} + x^{3} \left (\frac{a d^{2}}{3} + \frac{2 b c d}{3}\right ) + x^{2} \left (a c d + \frac{b c^{2}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(d*x+c)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.218163, size = 66, normalized size = 1.74 \[ \frac{1}{4} \, b d^{2} x^{4} + \frac{2}{3} \, b c d x^{3} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{2} \, b c^{2} x^{2} + a c d x^{2} + a c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)^2,x, algorithm="giac")
[Out]