Optimal. Leaf size=17 \[ \frac{(a+b x)^5}{5 b c} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.01148, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{(a+b x)^5}{5 b c} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/(a*c + b*c*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.3615, size = 10, normalized size = 0.59 \[ \frac{\left (a + b x\right )^{5}}{5 b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/(b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00239059, size = 17, normalized size = 1. \[ \frac{(a+b x)^5}{5 b c} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/(a*c + b*c*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 16, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{5}}{5\,bc}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/(b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34641, size = 65, normalized size = 3.82 \[ \frac{b^{4} x^{5} + 5 \, a b^{3} x^{4} + 10 \, a^{2} b^{2} x^{3} + 10 \, a^{3} b x^{2} + 5 \, a^{4} x}{5 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.191581, size = 65, normalized size = 3.82 \[ \frac{b^{4} x^{5} + 5 \, a b^{3} x^{4} + 10 \, a^{2} b^{2} x^{3} + 10 \, a^{3} b x^{2} + 5 \, a^{4} x}{5 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.19211, size = 51, normalized size = 3. \[ \frac{a^{4} x}{c} + \frac{2 a^{3} b x^{2}}{c} + \frac{2 a^{2} b^{2} x^{3}}{c} + \frac{a b^{3} x^{4}}{c} + \frac{b^{4} x^{5}}{5 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/(b*c*x+a*c),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.207892, size = 85, normalized size = 5. \[ \frac{b^{4} c^{4} x^{5} + 5 \, a b^{3} c^{4} x^{4} + 10 \, a^{2} b^{2} c^{4} x^{3} + 10 \, a^{3} b c^{4} x^{2} + 5 \, a^{4} c^{4} x}{5 \, c^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c),x, algorithm="giac")
[Out]