Optimal. Leaf size=390 \[ -\frac {3 b B^2 n^2 (c+d x)^2 \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )}{4 (a+b x)^2 (b c-a d)^2}+\frac {6 B^2 d n^2 (c+d x) \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )}{(a+b x) (b c-a d)^2}-\frac {3 b B n (c+d x)^2 \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )^2}{4 (a+b x)^2 (b c-a d)^2}+\frac {3 B d n (c+d x) \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )^2}{(a+b x) (b c-a d)^2}-\frac {b (c+d x)^2 \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )^3}{2 (a+b x)^2 (b c-a d)^2}+\frac {d (c+d x) \left (B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+A\right )^3}{(a+b x) (b c-a d)^2}-\frac {3 b B^3 n^3 (c+d x)^2}{8 (a+b x)^2 (b c-a d)^2}+\frac {6 B^3 d n^3 (c+d x)}{(a+b x) (b c-a d)^2} \]
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Rubi [B] time = 0.80, antiderivative size = 811, normalized size of antiderivative = 2.08, number of steps used = 21, number of rules used = 8, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.242, Rules used = {6742, 2492, 44, 2491, 2490, 32, 2509, 37} \[ -\frac {A^3}{2 b (a+b x)^2}+\frac {3 B d^2 n \log (a+b x) A^2}{2 b (b c-a d)^2}-\frac {3 B d^2 n \log (c+d x) A^2}{2 b (b c-a d)^2}-\frac {3 B \log \left (e (a+b x)^n (c+d x)^{-n}\right ) A^2}{2 b (a+b x)^2}+\frac {3 B d n A^2}{2 b (b c-a d) (a+b x)}-\frac {3 B n A^2}{4 b (a+b x)^2}-\frac {3 b B^2 n^2 (c+d x)^2 A}{4 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^2 (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right ) A}{2 (b c-a d)^2 (a+b x)^2}+\frac {3 B^2 d (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right ) A}{(b c-a d)^2 (a+b x)}-\frac {3 b B^2 n (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right ) A}{2 (b c-a d)^2 (a+b x)^2}+\frac {6 B^2 d n (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right ) A}{(b c-a d)^2 (a+b x)}+\frac {6 B^2 d n^2 A}{b (b c-a d) (a+b x)}-\frac {b B^3 (c+d x)^2 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {B^3 d (c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 b B^3 n^3 (c+d x)^2}{8 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {3 B^3 d n (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 b B^3 n^2 (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {6 B^3 d n^2 (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {6 B^3 d n^3}{b (b c-a d) (a+b x)} \]
Antiderivative was successfully verified.
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Rule 32
Rule 37
Rule 44
Rule 2490
Rule 2491
Rule 2492
Rule 2509
Rule 6742
Rubi steps
\begin {align*} \int \frac {\left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3}{(a+b x)^3} \, dx &=\int \left (\frac {A^3}{(a+b x)^3}+\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3}+\frac {3 A B^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3}+\frac {B^3 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3}\right ) \, dx\\ &=-\frac {A^3}{2 b (a+b x)^2}+\left (3 A^2 B\right ) \int \frac {\log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx+\left (3 A B^2\right ) \int \frac {\log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx+B^3 \int \frac {\log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx\\ &=-\frac {A^3}{2 b (a+b x)^2}-\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 b (a+b x)^2}+\frac {\left (3 A b B^2\right ) \int \frac {(c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx}{b c-a d}+\frac {\left (b B^3\right ) \int \frac {(c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx}{b c-a d}-\frac {\left (3 A B^2 d\right ) \int \frac {\log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx}{b c-a d}-\frac {\left (B^3 d\right ) \int \frac {\log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx}{b c-a d}+\frac {\left (3 A^2 B (b c-a d) n\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{2 b}\\ &=-\frac {A^3}{2 b (a+b x)^2}-\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 b (a+b x)^2}+\frac {3 A B^2 d (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {B^3 d (c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {b B^3 (c+d x)^2 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {\left (3 A b B^2 n\right ) \int \frac {(c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx}{b c-a d}+\frac {\left (3 b B^3 n\right ) \int \frac {(c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx}{2 (b c-a d)}-\frac {\left (6 A B^2 d n\right ) \int \frac {\log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx}{b c-a d}-\frac {\left (3 B^3 d n\right ) \int \frac {\log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx}{b c-a d}+\frac {\left (3 A^2 B (b c-a d) n\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^3}-\frac {b d}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2}{(b c-a d)^3 (a+b x)}-\frac {d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2 b}\\ &=-\frac {A^3}{2 b (a+b x)^2}-\frac {3 A^2 B n}{4 b (a+b x)^2}+\frac {3 A^2 B d n}{2 b (b c-a d) (a+b x)}+\frac {3 A^2 B d^2 n \log (a+b x)}{2 b (b c-a d)^2}-\frac {3 A^2 B d^2 n \log (c+d x)}{2 b (b c-a d)^2}-\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 b (a+b x)^2}+\frac {6 A B^2 d n (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 n (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {3 A B^2 d (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {3 B^3 d n (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {B^3 d (c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {b B^3 (c+d x)^2 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {\left (3 A b B^2 n^2\right ) \int \frac {c+d x}{(a+b x)^3} \, dx}{2 (b c-a d)}+\frac {\left (3 b B^3 n^2\right ) \int \frac {(c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^3} \, dx}{2 (b c-a d)}-\frac {\left (6 A B^2 d n^2\right ) \int \frac {1}{(a+b x)^2} \, dx}{b c-a d}-\frac {\left (6 B^3 d n^2\right ) \int \frac {\log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx}{b c-a d}\\ &=-\frac {A^3}{2 b (a+b x)^2}-\frac {3 A^2 B n}{4 b (a+b x)^2}+\frac {3 A^2 B d n}{2 b (b c-a d) (a+b x)}+\frac {6 A B^2 d n^2}{b (b c-a d) (a+b x)}-\frac {3 A b B^2 n^2 (c+d x)^2}{4 (b c-a d)^2 (a+b x)^2}+\frac {3 A^2 B d^2 n \log (a+b x)}{2 b (b c-a d)^2}-\frac {3 A^2 B d^2 n \log (c+d x)}{2 b (b c-a d)^2}-\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 b (a+b x)^2}+\frac {6 A B^2 d n (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {6 B^3 d n^2 (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 n (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n^2 (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {3 A B^2 d (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {3 B^3 d n (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {B^3 d (c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {b B^3 (c+d x)^2 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}+\frac {\left (3 b B^3 n^3\right ) \int \frac {c+d x}{(a+b x)^3} \, dx}{4 (b c-a d)}-\frac {\left (6 B^3 d n^3\right ) \int \frac {1}{(a+b x)^2} \, dx}{b c-a d}\\ &=-\frac {A^3}{2 b (a+b x)^2}-\frac {3 A^2 B n}{4 b (a+b x)^2}+\frac {3 A^2 B d n}{2 b (b c-a d) (a+b x)}+\frac {6 A B^2 d n^2}{b (b c-a d) (a+b x)}+\frac {6 B^3 d n^3}{b (b c-a d) (a+b x)}-\frac {3 A b B^2 n^2 (c+d x)^2}{4 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n^3 (c+d x)^2}{8 (b c-a d)^2 (a+b x)^2}+\frac {3 A^2 B d^2 n \log (a+b x)}{2 b (b c-a d)^2}-\frac {3 A^2 B d^2 n \log (c+d x)}{2 b (b c-a d)^2}-\frac {3 A^2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 b (a+b x)^2}+\frac {6 A B^2 d n (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {6 B^3 d n^2 (c+d x) \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 n (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n^2 (c+d x)^2 \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {3 A B^2 d (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}+\frac {3 B^3 d n (c+d x) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {3 A b B^2 (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}-\frac {3 b B^3 n (c+d x)^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )}{4 (b c-a d)^2 (a+b x)^2}+\frac {B^3 d (c+d x) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{(b c-a d)^2 (a+b x)}-\frac {b B^3 (c+d x)^2 \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )}{2 (b c-a d)^2 (a+b x)^2}\\ \end {align*}
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Mathematica [A] time = 1.18, size = 693, normalized size = 1.78 \[ -\frac {-6 B d^2 n (a+b x)^2 \log (a+b x) \left (2 B (2 A+3 B n) \log \left (e (a+b x)^n (c+d x)^{-n}\right )+2 B n \log (c+d x) \left (2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+2 A+3 B n\right )+2 B^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )+2 A^2+6 A B n+2 B^2 n^2 \log ^2(c+d x)+7 B^2 n^2\right )+6 B d^2 n (a+b x)^2 \log (c+d x) \left (2 B (2 A+3 B n) \log \left (e (a+b x)^n (c+d x)^{-n}\right )+2 B^2 \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )+2 A^2+6 A B n+7 B^2 n^2\right )+(b c-a d) \left (4 A^3 (b c-a d)+6 B \left (2 A^2 (b c-a d)+2 A B n (b (c-2 d x)-3 a d)+B^2 n^2 (b (c-6 d x)-7 a d)\right ) \log \left (e (a+b x)^n (c+d x)^{-n}\right )+6 A^2 B n (b (c-2 d x)-3 a d)+6 B^2 (2 A (b c-a d)+B n (b (c-2 d x)-3 a d)) \log ^2\left (e (a+b x)^n (c+d x)^{-n}\right )+6 A B^2 n^2 (b (c-6 d x)-7 a d)+4 B^3 (b c-a d) \log ^3\left (e (a+b x)^n (c+d x)^{-n}\right )+3 B^3 n^3 (b (c-14 d x)-15 a d)\right )+6 B^2 d^2 n^2 (a+b x)^2 \log ^2(a+b x) \left (2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+2 A+2 B n \log (c+d x)+3 B n\right )+6 B^2 d^2 n^2 (a+b x)^2 \log ^2(c+d x) \left (2 B \log \left (e (a+b x)^n (c+d x)^{-n}\right )+2 A+3 B n\right )+4 B^3 d^2 n^3 (a+b x)^2 \log ^3(c+d x)-4 B^3 d^2 n^3 (a+b x)^2 \log ^3(a+b x)}{8 b (a+b x)^2 (b c-a d)^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 2244, normalized size = 5.75 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (B \log \left (\frac {{\left (b x + a\right )}^{n} e}{{\left (d x + c\right )}^{n}}\right ) + A\right )}^{3}}{{\left (b x + a\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 32.82, size = 120138, normalized size = 308.05 \[ \text {output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.76, size = 2246, normalized size = 5.76 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.99, size = 966, normalized size = 2.48 \[ -{\ln \left (\frac {e\,{\left (a+b\,x\right )}^n}{{\left (c+d\,x\right )}^n}\right )}^3\,\left (\frac {B^3}{2\,b\,\left (a^2+2\,a\,b\,x+b^2\,x^2\right )}-\frac {B^3\,d^2}{2\,b\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}\right )-\frac {\frac {4\,A^3\,a\,d-4\,A^3\,b\,c+45\,B^3\,a\,d\,n^3-3\,B^3\,b\,c\,n^3+18\,A^2\,B\,a\,d\,n-6\,A^2\,B\,b\,c\,n+42\,A\,B^2\,a\,d\,n^2-6\,A\,B^2\,b\,c\,n^2}{2\,\left (a\,d-b\,c\right )}+\frac {3\,x\,\left (2\,b\,d\,A^2\,B\,n+6\,b\,d\,A\,B^2\,n^2+7\,b\,d\,B^3\,n^3\right )}{a\,d-b\,c}}{4\,a^2\,b+8\,a\,b^2\,x+4\,b^3\,x^2}-{\ln \left (\frac {e\,{\left (a+b\,x\right )}^n}{{\left (c+d\,x\right )}^n}\right )}^2\,\left (\frac {3\,A\,B^2}{2\,\left (a^2\,b+2\,a\,b^2\,x+b^3\,x^2\right )}-\frac {3\,d^2\,\left (3\,n\,B^3+2\,A\,B^2\right )}{4\,b\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}+\frac {3\,B^3\,d^2\,\left (\frac {b\,n\,\left (a\,d-b\,c\right )\,\left (2\,a\,d-b\,c\right )}{d^2}+\frac {2\,b^2\,n\,x\,\left (a\,d-b\,c\right )}{d}+\frac {a\,b\,n\,\left (a\,d-b\,c\right )}{d}\right )}{4\,b\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )\,\left (a^2\,b+2\,a\,b^2\,x+b^3\,x^2\right )}\right )-\ln \left (\frac {e\,{\left (a+b\,x\right )}^n}{{\left (c+d\,x\right )}^n}\right )\,\left (\frac {3\,B\,b\,d\,\left (A^2-B^2\,n^2\right )\,x^2+3\,B\,\left (a\,d+b\,c\right )\,\left (A^2-B^2\,n^2\right )\,x+3\,B\,a\,c\,\left (A^2-B^2\,n^2\right )}{2\,b\,{\left (a+b\,x\right )}^3\,\left (c+d\,x\right )}+\frac {3\,d^2\,\left (3\,n\,B^3+2\,A\,B^2\right )\,\left (x\,\left (\left (\frac {b\,n\,\left (a\,d-b\,c\right )\,\left (2\,a\,d-b\,c\right )}{d^2}+\frac {a\,b\,n\,\left (a\,d-b\,c\right )}{d}\right )\,\left (a\,d+b\,c\right )+\frac {2\,a\,b^2\,c\,n\,\left (a\,d-b\,c\right )}{d}\right )+x^2\,\left (b\,d\,\left (\frac {b\,n\,\left (a\,d-b\,c\right )\,\left (2\,a\,d-b\,c\right )}{d^2}+\frac {a\,b\,n\,\left (a\,d-b\,c\right )}{d}\right )+\frac {2\,b^2\,n\,\left (a\,d+b\,c\right )\,\left (a\,d-b\,c\right )}{d}\right )+a\,c\,\left (\frac {b\,n\,\left (a\,d-b\,c\right )\,\left (2\,a\,d-b\,c\right )}{d^2}+\frac {a\,b\,n\,\left (a\,d-b\,c\right )}{d}\right )+2\,b^3\,n\,x^3\,\left (a\,d-b\,c\right )\right )}{4\,b^2\,{\left (a+b\,x\right )}^3\,\left (c+d\,x\right )\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}\right )-\frac {B\,d^2\,n\,\mathrm {atan}\left (\frac {B\,d^2\,n\,\left (2\,b\,d\,x-\frac {b^3\,c^2-a^2\,b\,d^2}{b\,\left (a\,d-b\,c\right )}\right )\,\left (2\,A^2+6\,A\,B\,n+7\,B^2\,n^2\right )\,3{}\mathrm {i}}{\left (a\,d-b\,c\right )\,\left (6\,A^2\,B\,d^2\,n+18\,A\,B^2\,d^2\,n^2+21\,B^3\,d^2\,n^3\right )}\right )\,\left (2\,A^2+6\,A\,B\,n+7\,B^2\,n^2\right )\,3{}\mathrm {i}}{2\,b\,{\left (a\,d-b\,c\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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