Optimal. Leaf size=404 \[ \frac {2 b e^6 n \log \left (1-\frac {d}{d+\frac {e}{\sqrt {x}}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}+\frac {2 b e^5 n \sqrt {x} \left (d+\frac {e}{\sqrt {x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {2 b^2 e^6 n^2 \text {Li}_2\left (\frac {d}{d+\frac {e}{\sqrt {x}}}\right )}{3 d^6}+\frac {77 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{90 d^6}+\frac {137 b^2 e^6 n^2 \log (x)}{180 d^6}-\frac {77 b^2 e^5 n^2 \sqrt {x}}{90 d^5}+\frac {47 b^2 e^4 n^2 x}{180 d^4}-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2} \]
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Rubi [A] time = 1.01, antiderivative size = 428, normalized size of antiderivative = 1.06, number of steps used = 26, number of rules used = 12, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44} \[ \frac {2 b^2 e^6 n^2 \text {PolyLog}\left (2,\frac {e}{d \sqrt {x}}+1\right )}{3 d^6}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}-\frac {e^6 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2}{3 d^6}+\frac {2 b e^6 n \log \left (-\frac {e}{d \sqrt {x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}+\frac {2 b e^5 n \sqrt {x} \left (d+\frac {e}{\sqrt {x}}\right ) \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}-\frac {77 b^2 e^5 n^2 \sqrt {x}}{90 d^5}+\frac {47 b^2 e^4 n^2 x}{180 d^4}+\frac {77 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{90 d^6}+\frac {137 b^2 e^6 n^2 \log (x)}{180 d^6} \]
Antiderivative was successfully verified.
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Rule 31
Rule 44
Rule 2301
Rule 2314
Rule 2317
Rule 2319
Rule 2344
Rule 2347
Rule 2391
Rule 2398
Rule 2411
Rule 2454
Rubi steps
\begin {align*} \int x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2 \, dx &=-\left (2 \operatorname {Subst}\left (\int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{x^7} \, dx,x,\frac {1}{\sqrt {x}}\right )\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {1}{3} (2 b e n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c (d+e x)^n\right )}{x^6 (d+e x)} \, dx,x,\frac {1}{\sqrt {x}}\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {1}{3} (2 b n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^6} \, dx,x,d+\frac {e}{\sqrt {x}}\right )\\ &=\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {(2 b n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^6} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d}+\frac {(2 b e n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^5} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d}\\ &=\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {(2 b e n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^5} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^2}-\frac {\left (2 b e^2 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^4} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^2}-\frac {\left (2 b^2 e n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^5} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{15 d}\\ &=-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2-\frac {\left (2 b e^2 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^4} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^3}+\frac {\left (2 b e^3 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^3} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^3}-\frac {\left (2 b^2 e n^2\right ) \operatorname {Subst}\left (\int \left (-\frac {e^5}{d (d-x)^5}-\frac {e^5}{d^2 (d-x)^4}-\frac {e^5}{d^3 (d-x)^3}-\frac {e^5}{d^4 (d-x)^2}-\frac {e^5}{d^5 (d-x)}-\frac {e^5}{d^5 x}\right ) \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{15 d}+\frac {\left (b^2 e^2 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^4} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{6 d^2}\\ &=-\frac {2 b^2 e^5 n^2 \sqrt {x}}{15 d^5}+\frac {b^2 e^4 n^2 x}{15 d^4}-\frac {2 b^2 e^3 n^2 x^{3/2}}{45 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}+\frac {2 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{15 d^6}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {b^2 e^6 n^2 \log (x)}{15 d^6}+\frac {\left (2 b e^3 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^3} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^4}-\frac {\left (2 b e^4 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^4}+\frac {\left (b^2 e^2 n^2\right ) \operatorname {Subst}\left (\int \left (\frac {e^4}{d (d-x)^4}+\frac {e^4}{d^2 (d-x)^3}+\frac {e^4}{d^3 (d-x)^2}+\frac {e^4}{d^4 (d-x)}+\frac {e^4}{d^4 x}\right ) \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{6 d^2}-\frac {\left (2 b^2 e^3 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^3} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{9 d^3}\\ &=-\frac {3 b^2 e^5 n^2 \sqrt {x}}{10 d^5}+\frac {3 b^2 e^4 n^2 x}{20 d^4}-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}+\frac {3 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{10 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {3 b^2 e^6 n^2 \log (x)}{20 d^6}-\frac {\left (2 b e^4 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^5}+\frac {\left (2 b e^5 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \left (-\frac {d}{e}+\frac {x}{e}\right )} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^5}-\frac {\left (2 b^2 e^3 n^2\right ) \operatorname {Subst}\left (\int \left (-\frac {e^3}{d (d-x)^3}-\frac {e^3}{d^2 (d-x)^2}-\frac {e^3}{d^3 (d-x)}-\frac {e^3}{d^3 x}\right ) \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{9 d^3}+\frac {\left (b^2 e^4 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \left (-\frac {d}{e}+\frac {x}{e}\right )^2} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^4}\\ &=-\frac {47 b^2 e^5 n^2 \sqrt {x}}{90 d^5}+\frac {47 b^2 e^4 n^2 x}{180 d^4}-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}+\frac {47 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{90 d^6}+\frac {2 b e^5 n \left (d+\frac {e}{\sqrt {x}}\right ) \sqrt {x} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {47 b^2 e^6 n^2 \log (x)}{180 d^6}+\frac {\left (2 b e^5 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^6}-\frac {\left (2 b e^6 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^6}+\frac {\left (b^2 e^4 n^2\right ) \operatorname {Subst}\left (\int \left (\frac {e^2}{d (d-x)^2}+\frac {e^2}{d^2 (d-x)}+\frac {e^2}{d^2 x}\right ) \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^4}-\frac {\left (2 b^2 e^5 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {d}{e}+\frac {x}{e}} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^6}\\ &=-\frac {77 b^2 e^5 n^2 \sqrt {x}}{90 d^5}+\frac {47 b^2 e^4 n^2 x}{180 d^4}-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}+\frac {77 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{90 d^6}+\frac {2 b e^5 n \left (d+\frac {e}{\sqrt {x}}\right ) \sqrt {x} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}-\frac {e^6 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2}{3 d^6}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {2 b e^6 n \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right ) \log \left (-\frac {e}{d \sqrt {x}}\right )}{3 d^6}+\frac {137 b^2 e^6 n^2 \log (x)}{180 d^6}-\frac {\left (2 b^2 e^6 n^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {x}{d}\right )}{x} \, dx,x,d+\frac {e}{\sqrt {x}}\right )}{3 d^6}\\ &=-\frac {77 b^2 e^5 n^2 \sqrt {x}}{90 d^5}+\frac {47 b^2 e^4 n^2 x}{180 d^4}-\frac {b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac {b^2 e^2 n^2 x^2}{30 d^2}+\frac {77 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )}{90 d^6}+\frac {2 b e^5 n \left (d+\frac {e}{\sqrt {x}}\right ) \sqrt {x} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^6}-\frac {b e^4 n x \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{3 d^4}+\frac {2 b e^3 n x^{3/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{9 d^3}-\frac {b e^2 n x^2 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{6 d^2}+\frac {2 b e n x^{5/2} \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )}{15 d}-\frac {e^6 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2}{3 d^6}+\frac {1}{3} x^3 \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right )^2+\frac {2 b e^6 n \left (a+b \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )\right ) \log \left (-\frac {e}{d \sqrt {x}}\right )}{3 d^6}+\frac {137 b^2 e^6 n^2 \log (x)}{180 d^6}+\frac {2 b^2 e^6 n^2 \text {Li}_2\left (1+\frac {e}{d \sqrt {x}}\right )}{3 d^6}\\ \end {align*}
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Mathematica [A] time = 0.27, size = 540, normalized size = 1.34 \[ \frac {60 a^2 d^6 x^3+120 a b d^6 x^3 \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )+24 a b d^5 e n x^{5/2}-30 a b d^4 e^2 n x^2+40 a b d^3 e^3 n x^{3/2}-60 a b d^2 e^4 n x-120 a b e^6 n \log \left (d \sqrt {x}+e\right )+120 a b d e^5 n \sqrt {x}+60 b^2 d^6 x^3 \log ^2\left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )+24 b^2 d^5 e n x^{5/2} \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )-30 b^2 d^4 e^2 n x^2 \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )+40 b^2 d^3 e^3 n x^{3/2} \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )-60 b^2 d^2 e^4 n x \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )-120 b^2 e^6 n \log \left (d \sqrt {x}+e\right ) \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )+120 b^2 d e^5 n \sqrt {x} \log \left (c \left (d+\frac {e}{\sqrt {x}}\right )^n\right )+6 b^2 d^4 e^2 n^2 x^2-18 b^2 d^3 e^3 n^2 x^{3/2}+47 b^2 d^2 e^4 n^2 x-120 b^2 e^6 n^2 \text {Li}_2\left (\frac {\sqrt {x} d}{e}+1\right )+60 b^2 e^6 n^2 \log ^2\left (d \sqrt {x}+e\right )+214 b^2 e^6 n^2 \log \left (d+\frac {e}{\sqrt {x}}\right )+60 b^2 e^6 n^2 \log \left (d \sqrt {x}+e\right )-120 b^2 e^6 n^2 \log \left (d \sqrt {x}+e\right ) \log \left (-\frac {d \sqrt {x}}{e}\right )-154 b^2 d e^5 n^2 \sqrt {x}+107 b^2 e^6 n^2 \log (x)}{180 d^6} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (b^{2} x^{2} \log \left (c \left (\frac {d x + e \sqrt {x}}{x}\right )^{n}\right )^{2} + 2 \, a b x^{2} \log \left (c \left (\frac {d x + e \sqrt {x}}{x}\right )^{n}\right ) + a^{2} x^{2}, x\right ) \]
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 \[ \int {\left (b \log \left (c {\left (d + \frac {e}{\sqrt {x}}\right )}^{n}\right ) + a\right )}^{2} x^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.10, size = 0, normalized size = 0.00 \[ \int \left (b \ln \left (c \left (d +\frac {e}{\sqrt {x}}\right )^{n}\right )+a \right )^{2} x^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {1}{3} \, b^{2} n^{2} x^{3} \log \left (d \sqrt {x} + e\right )^{2} - \int -\frac {3 \, {\left (b^{2} d \log \relax (c)^{2} + 2 \, a b d \log \relax (c) + a^{2} d\right )} x^{3} + 3 \, {\left (b^{2} e \log \relax (c)^{2} + 2 \, a b e \log \relax (c) + a^{2} e\right )} x^{\frac {5}{2}} - {\left (b^{2} d n x^{3} - 6 \, {\left (b^{2} d \log \relax (c) + a b d\right )} x^{3} - 6 \, {\left (b^{2} e \log \relax (c) + a b e\right )} x^{\frac {5}{2}} + 6 \, {\left (b^{2} d x^{3} + b^{2} e x^{\frac {5}{2}}\right )} \log \left (x^{\frac {1}{2} \, n}\right )\right )} n \log \left (d \sqrt {x} + e\right ) + 3 \, {\left (b^{2} d x^{3} + b^{2} e x^{\frac {5}{2}}\right )} \log \left (x^{\frac {1}{2} \, n}\right )^{2} - 6 \, {\left ({\left (b^{2} d \log \relax (c) + a b d\right )} x^{3} + {\left (b^{2} e \log \relax (c) + a b e\right )} x^{\frac {5}{2}}\right )} \log \left (x^{\frac {1}{2} \, n}\right )}{3 \, {\left (d x + e \sqrt {x}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int x^2\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{\sqrt {x}}\right )}^n\right )\right )}^2 \,d x \]
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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