Optimal. Leaf size=14 \[ -\frac {1}{3 b (c+d x)^3} \]
[Out]
________________________________________________________________________________________
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]
________________________________________________________________________________________
Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(36\) vs. \(2(14)=28\).
time = 1.85, size = 34, normalized size = 2.43 \begin {gather*} -\frac {1}{3 b \left (c^3+3 c^2 d x+3 c d^2 x^2+d^3 x^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.15, size = 13, normalized size = 0.93
method | result | size |
gosper | \(-\frac {1}{3 b \left (d x +c \right )^{3}}\) | \(13\) |
default | \(-\frac {1}{3 b \left (d x +c \right )^{3}}\) | \(13\) |
norman | \(-\frac {1}{3 b \left (d x +c \right )^{3}}\) | \(13\) |
risch | \(-\frac {1}{3 b \left (d x +c \right )^{3}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 36 vs.
\(2 (12) = 24\).
time = 0.26, 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]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 36 vs.
\(2 (12) = 24\).
time = 0.29, 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]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (12) = 24\).
time = 0.14, 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]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} -\frac 1{3 b \left (x d+c\right )^{3}} \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]
________________________________________________________________________________________