Optimal. Leaf size=14 \[ -\frac {1}{3 b (c+d x)^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {21, 32} \begin {gather*} -\frac {1}{3 b (c+d x)^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 21
Rule 32
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b c}{d}+b x\right ) (c+d x)^3} \, dx &=\frac {d \int \frac {1}{(c+d x)^4} \, dx}{b}\\ &=-\frac {1}{3 b (c+d x)^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {1}{3 b (c+d x)^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (\frac {b c}{d}+b x\right ) (c+d x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.29, size = 36, normalized size = 2.57 \begin {gather*} -\frac {1}{3 \, {\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.14, size = 12, normalized size = 0.86 \begin {gather*} -\frac {1}{3 \, {\left (d x + c\right )}^{3} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} -\frac {1}{3 \left (d x +c \right )^{3} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.34, size = 36, normalized size = 2.57 \begin {gather*} -\frac {1}{3 \, {\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 38, normalized size = 2.71 \begin {gather*} -\frac {1}{3\,b\,c^3+9\,b\,c^2\,d\,x+9\,b\,c\,d^2\,x^2+3\,b\,d^3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.28, size = 44, normalized size = 3.14 \begin {gather*} - \frac {d}{3 b c^{3} d + 9 b c^{2} d^{2} x + 9 b c d^{3} x^{2} + 3 b d^{4} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________