Optimal. Leaf size=35 \[ -\frac {\text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b c-a d} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6745}
\begin {gather*} -\frac {\text {PolyLog}\left (3,\frac {b c-a d}{d (a+b x)}+1\right )}{b c-a d} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6745
Rubi steps
\begin {align*} \int \frac {\text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{(a+b x) (c+d x)} \, dx &=-\frac {\text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b c-a d}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 30, normalized size = 0.86 \begin {gather*} \frac {\text {Li}_3\left (\frac {b (c+d x)}{d (a+b x)}\right )}{-b c+a d} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.68, size = 36, normalized size = 1.03
method | result | size |
derivativedivides | \(\frac {\polylog \left (3, 1-\frac {a d -c b}{d \left (b x +a \right )}\right )}{a d -c b}\) | \(36\) |
default | \(\frac {\polylog \left (3, 1-\frac {a d -c b}{d \left (b x +a \right )}\right )}{a d -c b}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {Li}_{2}\left (- \frac {a d}{a d + b d x} + \frac {b c}{a d + b d x} + 1\right )}{\left (a + b x\right ) \left (c + d x\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\mathrm {polylog}\left (2,1-\frac {a\,d-b\,c}{d\,\left (a+b\,x\right )}\right )}{\left (a+b\,x\right )\,\left (c+d\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________