Optimal. Leaf size=23 \[ \frac{\left (a+b (c+d x)^4\right )^2}{8 b d} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0231063, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{\left (a+b (c+d x)^4\right )^2}{8 b d} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^3*(a + b*(c + d*x)^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b \int ^{\left (c + d x\right )^{4}} x\, dx}{4 d} + \frac{\int ^{\left (c + d x\right )^{4}} a\, dx}{4 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**3*(a+b*(d*x+c)**4),x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.0321177, size = 80, normalized size = 3.48 \[ \frac{1}{8} x \left (4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right ) \left (2 a+b \left (2 c^4+4 c^3 d x+6 c^2 d^2 x^2+4 c d^3 x^3+d^4 x^4\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^3*(a + b*(c + d*x)^4),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.001, size = 136, normalized size = 5.9 \[{\frac{{d}^{7}b{x}^{8}}{8}}+c{d}^{6}b{x}^{7}+{\frac{7\,{c}^{2}{d}^{5}b{x}^{6}}{2}}+7\,{c}^{3}b{d}^{4}{x}^{5}+{\frac{ \left ( 34\,{c}^{4}b{d}^{3}+{d}^{3} \left ( b{c}^{4}+a \right ) \right ){x}^{4}}{4}}+{\frac{ \left ( 18\,{c}^{5}{d}^{2}b+3\,c{d}^{2} \left ( b{c}^{4}+a \right ) \right ){x}^{3}}{3}}+{\frac{ \left ( 4\,{c}^{6}db+3\,{c}^{2}d \left ( b{c}^{4}+a \right ) \right ){x}^{2}}{2}}+{c}^{3} \left ( b{c}^{4}+a \right ) x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^3*(a+b*(d*x+c)^4),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36092, size = 28, normalized size = 1.22 \[ \frac{{\left ({\left (d x + c\right )}^{4} b + a\right )}^{2}}{8 \, b d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((d*x + c)^4*b + a)*(d*x + c)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.181301, size = 1, normalized size = 0.04 \[ \frac{1}{8} x^{8} d^{7} b + x^{7} d^{6} c b + \frac{7}{2} x^{6} d^{5} c^{2} b + 7 x^{5} d^{4} c^{3} b + \frac{35}{4} x^{4} d^{3} c^{4} b + 7 x^{3} d^{2} c^{5} b + \frac{7}{2} x^{2} d c^{6} b + x c^{7} b + \frac{1}{4} x^{4} d^{3} a + x^{3} d^{2} c a + \frac{3}{2} x^{2} d c^{2} a + x c^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((d*x + c)^4*b + a)*(d*x + c)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.16641, size = 126, normalized size = 5.48 \[ 7 b c^{3} d^{4} x^{5} + \frac{7 b c^{2} d^{5} x^{6}}{2} + b c d^{6} x^{7} + \frac{b d^{7} x^{8}}{8} + x^{4} \left (\frac{a d^{3}}{4} + \frac{35 b c^{4} d^{3}}{4}\right ) + x^{3} \left (a c d^{2} + 7 b c^{5} d^{2}\right ) + x^{2} \left (\frac{3 a c^{2} d}{2} + \frac{7 b c^{6} d}{2}\right ) + x \left (a c^{3} + b c^{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**3*(a+b*(d*x+c)**4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213079, size = 34, normalized size = 1.48 \[ \frac{{\left (d x + c\right )}^{8} b + 2 \,{\left (d x + c\right )}^{4} a}{8 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((d*x + c)^4*b + a)*(d*x + c)^3,x, algorithm="giac")
[Out]