Optimal. Leaf size=273 \[ -\frac {B d^2 n (a+b x)}{(b c-a d)^3 g^2 i^2 (c+d x)}-\frac {b^2 B n (c+d x)}{(b c-a d)^3 g^2 i^2 (a+b x)}+\frac {d^2 (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 g^2 i^2 (c+d x)}-\frac {b^2 (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 g^2 i^2 (a+b x)}-\frac {2 b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log \left (\frac {a+b x}{c+d x}\right )}{(b c-a d)^3 g^2 i^2}+\frac {b B d n \log ^2\left (\frac {a+b x}{c+d x}\right )}{(b c-a d)^3 g^2 i^2} \]
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Rubi [A]
time = 0.15, antiderivative size = 273, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 4, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.093, Rules used = {2561, 45, 2372,
2338} \begin {gather*} -\frac {b^2 (c+d x) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{g^2 i^2 (a+b x) (b c-a d)^3}+\frac {d^2 (a+b x) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac {2 b d \log \left (\frac {a+b x}{c+d x}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{g^2 i^2 (b c-a d)^3}-\frac {b^2 B n (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac {B d^2 n (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac {b B d n \log ^2\left (\frac {a+b x}{c+d x}\right )}{g^2 i^2 (b c-a d)^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 2338
Rule 2372
Rule 2561
Rubi steps
\begin {align*} \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(148 c+148 d x)^2 (a g+b g x)^2} \, dx &=\int \left (\frac {b^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)^2}-\frac {b^2 d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2 (a+b x)}+\frac {d^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)^2}+\frac {b d^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2 (c+d x)}\right ) \, dx\\ &=-\frac {\left (b^2 d\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {\left (b d^2\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {b^2 \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{21904 (b c-a d)^2 g^2}+\frac {d^2 \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(c+d x)^2} \, dx}{21904 (b c-a d)^2 g^2}\\ &=-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}-\frac {(b B d n) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {(b B n) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{21904 (b c-a d)^2 g^2}+\frac {(B d n) \int \frac {b c-a d}{(a+b x) (c+d x)^2} \, dx}{21904 (b c-a d)^2 g^2}\\ &=-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{10952 (b c-a d)^3 g^2}-\frac {(b B d n) \int \left (\frac {b \log (c+d x)}{a+b x}-\frac {d \log (c+d x)}{c+d x}\right ) \, dx}{10952 (b c-a d)^3 g^2}+\frac {(b B n) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{21904 (b c-a d) g^2}+\frac {(B d n) \int \frac {1}{(a+b x) (c+d x)^2} \, dx}{21904 (b c-a d) g^2}\\ &=-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {\left (b^2 B d n\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}-\frac {\left (b^2 B d n\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}-\frac {\left (b B d^2 n\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {\left (b B d^2 n\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {(b B n) \int \left (\frac {b}{(b c-a d) (a+b x)^2}-\frac {b d}{(b c-a d)^2 (a+b x)}+\frac {d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{21904 (b c-a d) g^2}+\frac {(B d n) \int \left (\frac {b^2}{(b c-a d)^2 (a+b x)}-\frac {d}{(b c-a d) (c+d x)^2}-\frac {b d}{(b c-a d)^2 (c+d x)}\right ) \, dx}{21904 (b c-a d) g^2}\\ &=-\frac {b B n}{21904 (b c-a d)^2 g^2 (a+b x)}+\frac {B d n}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}-\frac {b B d n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}-\frac {b B d n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{10952 (b c-a d)^3 g^2}+\frac {\left (b^2 B d n\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{10952 (b c-a d)^3 g^2}+\frac {\left (b B d^2 n\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{10952 (b c-a d)^3 g^2}\\ &=-\frac {b B n}{21904 (b c-a d)^2 g^2 (a+b x)}+\frac {B d n}{21904 (b c-a d)^2 g^2 (c+d x)}+\frac {b B d n \log ^2(a+b x)}{21904 (b c-a d)^3 g^2}-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}-\frac {b B d n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {b B d n \log ^2(c+d x)}{21904 (b c-a d)^3 g^2}-\frac {b B d n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{10952 (b c-a d)^3 g^2}+\frac {(b B d n) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{10952 (b c-a d)^3 g^2}\\ &=-\frac {b B n}{21904 (b c-a d)^2 g^2 (a+b x)}+\frac {B d n}{21904 (b c-a d)^2 g^2 (c+d x)}+\frac {b B d n \log ^2(a+b x)}{21904 (b c-a d)^3 g^2}-\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{21904 (b c-a d)^2 g^2 (c+d x)}-\frac {b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{10952 (b c-a d)^3 g^2}-\frac {b B d n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{10952 (b c-a d)^3 g^2}+\frac {b B d n \log ^2(c+d x)}{21904 (b c-a d)^3 g^2}-\frac {b B d n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{10952 (b c-a d)^3 g^2}-\frac {b B d n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{10952 (b c-a d)^3 g^2}-\frac {b B d n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{10952 (b c-a d)^3 g^2}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 0.30, size = 342, normalized size = 1.25 \begin {gather*} \frac {-\frac {b^2 B c n}{a+b x}+\frac {a b B d n}{a+b x}+\frac {b B c d n}{c+d x}-\frac {a B d^2 n}{c+d x}-\frac {b (b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x}+\frac {d (-b c+a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{c+d x}-2 b d \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )+2 b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)+b B d n \left (\log (a+b x) \left (\log (a+b x)-2 \log \left (\frac {b (c+d x)}{b c-a d}\right )\right )-2 \text {Li}_2\left (\frac {d (a+b x)}{-b c+a d}\right )\right )-b B d n \left (\left (2 \log \left (\frac {d (a+b x)}{-b c+a d}\right )-\log (c+d x)\right ) \log (c+d x)+2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )\right )}{(b c-a d)^3 g^2 i^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.17, size = 0, normalized size = 0.00 \[\int \frac {A +B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )}{\left (b g x +a g \right )^{2} \left (d i x +c i \right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 794 vs.
\(2 (257) = 514\).
time = 0.32, size = 794, normalized size = 2.91 \begin {gather*} B {\left (\frac {2 \, b d x + b c + a d}{{\left (b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} g^{2} x^{2} + {\left (b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right )} g^{2} x + {\left (a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} g^{2}} + \frac {2 \, b d \log \left (b x + a\right )}{{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} g^{2}} - \frac {2 \, b d \log \left (d x + c\right )}{{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} g^{2}}\right )} \log \left ({\left (\frac {b x}{d x + c} + \frac {a}{d x + c}\right )}^{n} e\right ) + \frac {{\left (b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left (b^{2} d^{2} x^{2} + a b c d + {\left (b^{2} c d + a b d^{2}\right )} x\right )} \log \left (b x + a\right )^{2} + 2 \, {\left (b^{2} d^{2} x^{2} + a b c d + {\left (b^{2} c d + a b d^{2}\right )} x\right )} \log \left (b x + a\right ) \log \left (d x + c\right ) - {\left (b^{2} d^{2} x^{2} + a b c d + {\left (b^{2} c d + a b d^{2}\right )} x\right )} \log \left (d x + c\right )^{2}\right )} B n}{a b^{3} c^{4} g^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} - a^{4} c d^{3} g^{2} + {\left (b^{4} c^{3} d g^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} - a^{3} b d^{4} g^{2}\right )} x^{2} + {\left (b^{4} c^{4} g^{2} - 2 \, a b^{3} c^{3} d g^{2} + 2 \, a^{3} b c d^{3} g^{2} - a^{4} d^{4} g^{2}\right )} x} + A {\left (\frac {2 \, b d x + b c + a d}{{\left (b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} g^{2} x^{2} + {\left (b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right )} g^{2} x + {\left (a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} g^{2}} + \frac {2 \, b d \log \left (b x + a\right )}{{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} g^{2}} - \frac {2 \, b d \log \left (d x + c\right )}{{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} g^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 365, normalized size = 1.34 \begin {gather*} \frac {{\left (A + B\right )} b^{2} c^{2} - {\left (A + B\right )} a^{2} d^{2} + {\left (B b^{2} d^{2} n x^{2} + B a b c d n + {\left (B b^{2} c d + B a b d^{2}\right )} n x\right )} \log \left (\frac {b x + a}{d x + c}\right )^{2} + {\left (B b^{2} c^{2} - 2 \, B a b c d + B a^{2} d^{2}\right )} n + 2 \, {\left ({\left (A + B\right )} b^{2} c d - {\left (A + B\right )} a b d^{2}\right )} x + {\left (2 \, {\left (A + B\right )} b^{2} d^{2} x^{2} + 2 \, {\left (A + B\right )} a b c d + {\left (B b^{2} c^{2} - B a^{2} d^{2}\right )} n + 2 \, {\left ({\left (A + B\right )} b^{2} c d + {\left (A + B\right )} a b d^{2} + {\left (B b^{2} c d - B a b d^{2}\right )} n\right )} x\right )} \log \left (\frac {b x + a}{d x + c}\right )}{{\left (b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right )} g^{2} x^{2} + {\left (b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right )} g^{2} x + {\left (a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right )} g^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 95.65, size = 86, normalized size = 0.32 \begin {gather*} {\left (\frac {{\left (d x + c\right )} B n \log \left (\frac {b x + a}{d x + c}\right )}{{\left (b x + a\right )} g^{2}} + \frac {{\left (B n + A + B\right )} {\left (d x + c\right )}}{{\left (b x + a\right )} g^{2}}\right )} {\left (\frac {b c}{{\left (b c - a d\right )}^{2}} - \frac {a d}{{\left (b c - a d\right )}^{2}}\right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.46, size = 432, normalized size = 1.58 \begin {gather*} \frac {B\,b\,d\,{\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )}^2}{g^2\,i^2\,n\,{\left (a\,d-b\,c\right )}^3}-\frac {A\,b\,c}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {A\,a\,d}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}+\frac {B\,a\,d\,n}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {B\,b\,c\,n}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {2\,A\,b\,d\,x}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {B\,a\,d\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {B\,b\,c\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {2\,B\,b\,d\,x\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^2\,\left (a+b\,x\right )\,\left (c+d\,x\right )}-\frac {A\,b\,d\,\mathrm {atan}\left (\frac {a\,d\,1{}\mathrm {i}+b\,c\,1{}\mathrm {i}+b\,d\,x\,2{}\mathrm {i}}{a\,d-b\,c}\right )\,4{}\mathrm {i}}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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