Optimal. Leaf size=510 \[ \frac {8 b n (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}-\frac {8 b n \sqrt {f+g x} (e f-d g) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {8 b^2 n^2 (e f-d g)^{3/2} \text {Li}_2\left (1-\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}-\frac {8 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {64 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}+\frac {16 b^2 n^2 (e f-d g)^{3/2} \log \left (\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right ) \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{3 e^{3/2} g}+\frac {64 b^2 n^2 \sqrt {f+g x} (e f-d g)}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g} \]
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Rubi [A] time = 1.50, antiderivative size = 510, normalized size of antiderivative = 1.00, number of steps used = 21, number of rules used = 15, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.577, Rules used = {2398, 2411, 2346, 63, 208, 2348, 12, 1587, 6741, 5984, 5918, 2402, 2315, 2319, 50} \[ \frac {8 b^2 n^2 (e f-d g)^{3/2} \text {PolyLog}\left (2,1-\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}+\frac {8 b n (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}-\frac {8 b n \sqrt {f+g x} (e f-d g) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {8 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {64 b^2 n^2 (e f-d g)^{3/2} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}+\frac {16 b^2 n^2 (e f-d g)^{3/2} \log \left (\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right ) \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{3 e^{3/2} g}+\frac {64 b^2 n^2 \sqrt {f+g x} (e f-d g)}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g} \]
Antiderivative was successfully verified.
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Rule 12
Rule 50
Rule 63
Rule 208
Rule 1587
Rule 2315
Rule 2319
Rule 2346
Rule 2348
Rule 2398
Rule 2402
Rule 2411
Rule 5918
Rule 5984
Rule 6741
Rubi steps
\begin {align*} \int \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx &=\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {(4 b e n) \int \frac {(f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{d+e x} \, dx}{3 g}\\ &=\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {(4 b n) \operatorname {Subst}\left (\int \frac {\left (\frac {e f-d g}{e}+\frac {g x}{e}\right )^{3/2} \left (a+b \log \left (c x^n\right )\right )}{x} \, dx,x,d+e x\right )}{3 g}\\ &=\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {(4 b n) \operatorname {Subst}\left (\int \sqrt {\frac {e f-d g}{e}+\frac {g x}{e}} \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{3 e}-\frac {(4 b (e f-d g) n) \operatorname {Subst}\left (\int \frac {\sqrt {\frac {e f-d g}{e}+\frac {g x}{e}} \left (a+b \log \left (c x^n\right )\right )}{x} \, dx,x,d+e x\right )}{3 e g}\\ &=-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {(4 b (e f-d g) n) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{\sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}} \, dx,x,d+e x\right )}{3 e^2}-\frac {\left (4 b (e f-d g)^2 n\right ) \operatorname {Subst}\left (\int \frac {a+b \log \left (c x^n\right )}{x \sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}} \, dx,x,d+e x\right )}{3 e^2 g}+\frac {\left (8 b^2 n^2\right ) \operatorname {Subst}\left (\int \frac {\left (\frac {e f-d g}{e}+\frac {g x}{e}\right )^{3/2}}{x} \, dx,x,d+e x\right )}{9 g}\\ &=\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {\left (8 b^2 (e f-d g) n^2\right ) \operatorname {Subst}\left (\int \frac {\sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}}{x} \, dx,x,d+e x\right )}{9 e g}+\frac {\left (8 b^2 (e f-d g) n^2\right ) \operatorname {Subst}\left (\int \frac {\sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}}{x} \, dx,x,d+e x\right )}{3 e g}+\frac {\left (4 b^2 (e f-d g)^2 n^2\right ) \operatorname {Subst}\left (\int -\frac {2 \sqrt {e} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f-\frac {d g}{e}+\frac {g x}{e}}}{\sqrt {e f-d g}}\right )}{\sqrt {e f-d g} x} \, dx,x,d+e x\right )}{3 e^2 g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {\left (8 b^2 (e f-d g)^{3/2} n^2\right ) \operatorname {Subst}\left (\int \frac {\tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f-\frac {d g}{e}+\frac {g x}{e}}}{\sqrt {e f-d g}}\right )}{x} \, dx,x,d+e x\right )}{3 e^{3/2} g}+\frac {\left (8 b^2 (e f-d g)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}} \, dx,x,d+e x\right )}{9 e^2 g}+\frac {\left (8 b^2 (e f-d g)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{x \sqrt {\frac {e f-d g}{e}+\frac {g x}{e}}} \, dx,x,d+e x\right )}{3 e^2 g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {\left (16 b^2 (e f-d g)^{3/2} n^2\right ) \operatorname {Subst}\left (\int \frac {x \tanh ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {e f-d g}}\right )}{d g+e \left (-f+x^2\right )} \, dx,x,\sqrt {f+g x}\right )}{3 \sqrt {e} g}+\frac {\left (16 b^2 (e f-d g)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {e f-d g}{g}+\frac {e x^2}{g}} \, dx,x,\sqrt {f+g x}\right )}{9 e g^2}+\frac {\left (16 b^2 (e f-d g)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {e f-d g}{g}+\frac {e x^2}{g}} \, dx,x,\sqrt {f+g x}\right )}{3 e g^2}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {64 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}-\frac {\left (16 b^2 (e f-d g)^{3/2} n^2\right ) \operatorname {Subst}\left (\int \frac {x \tanh ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {e f-d g}}\right )}{-e f+d g+e x^2} \, dx,x,\sqrt {f+g x}\right )}{3 \sqrt {e} g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {64 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}-\frac {8 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {\left (16 b^2 (e f-d g) n^2\right ) \operatorname {Subst}\left (\int \frac {\tanh ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {e f-d g}}\right )}{1-\frac {\sqrt {e} x}{\sqrt {e f-d g}}} \, dx,x,\sqrt {f+g x}\right )}{3 e g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {64 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}-\frac {8 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {16 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \log \left (\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}-\frac {\left (16 b^2 (e f-d g) n^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {2}{1-\frac {\sqrt {e} x}{\sqrt {e f-d g}}}\right )}{1-\frac {e x^2}{e f-d g}} \, dx,x,\sqrt {f+g x}\right )}{3 e g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {64 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}-\frac {8 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {16 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \log \left (\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}+\frac {\left (16 b^2 (e f-d g)^{3/2} n^2\right ) \operatorname {Subst}\left (\int \frac {\log (2 x)}{1-2 x} \, dx,x,\frac {1}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}\\ &=\frac {64 b^2 (e f-d g) n^2 \sqrt {f+g x}}{9 e g}+\frac {16 b^2 n^2 (f+g x)^{3/2}}{27 g}-\frac {64 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )}{9 e^{3/2} g}-\frac {8 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )^2}{3 e^{3/2} g}-\frac {8 b (e f-d g) n \sqrt {f+g x} \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e g}-\frac {8 b n (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )}{9 g}+\frac {8 b (e f-d g)^{3/2} n \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{3 e^{3/2} g}+\frac {2 (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{3 g}+\frac {16 b^2 (e f-d g)^{3/2} n^2 \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right ) \log \left (\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}+\frac {8 b^2 (e f-d g)^{3/2} n^2 \text {Li}_2\left (1-\frac {2}{1-\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}}\right )}{3 e^{3/2} g}\\ \end {align*}
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Mathematica [A] time = 1.17, size = 643, normalized size = 1.26 \[ \frac {2 \left ((f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )^2-\frac {b n \left (12 e^{3/2} (f+g x)^{3/2} \left (a+b \log \left (c (d+e x)^n\right )\right )+18 (e f-d g)^{3/2} \log \left (\sqrt {e f-d g}-\sqrt {e} \sqrt {f+g x}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )-18 (e f-d g)^{3/2} \log \left (\sqrt {e f-d g}+\sqrt {e} \sqrt {f+g x}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )+36 a \sqrt {e} \sqrt {f+g x} (e f-d g)+36 b \sqrt {e} \sqrt {f+g x} (e f-d g) \log \left (c (d+e x)^n\right )-9 b n (e f-d g)^{3/2} \left (2 \text {Li}_2\left (\frac {1}{2}-\frac {\sqrt {e} \sqrt {f+g x}}{2 \sqrt {e f-d g}}\right )+\log \left (\sqrt {e f-d g}-\sqrt {e} \sqrt {f+g x}\right ) \left (\log \left (\sqrt {e f-d g}-\sqrt {e} \sqrt {f+g x}\right )+2 \log \left (\frac {1}{2} \left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}+1\right )\right )\right )\right )+9 b n (e f-d g)^{3/2} \left (2 \text {Li}_2\left (\frac {1}{2} \left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}+1\right )\right )+\log \left (\sqrt {e f-d g}+\sqrt {e} \sqrt {f+g x}\right ) \left (\log \left (\sqrt {e f-d g}+\sqrt {e} \sqrt {f+g x}\right )+2 \log \left (\frac {1}{2}-\frac {\sqrt {e} \sqrt {f+g x}}{2 \sqrt {e f-d g}}\right )\right )\right )-96 b n (e f-d g) \left (\sqrt {e} \sqrt {f+g x}-\sqrt {e f-d g} \tanh ^{-1}\left (\frac {\sqrt {e} \sqrt {f+g x}}{\sqrt {e f-d g}}\right )\right )-8 b e^{3/2} n (f+g x)^{3/2}\right )}{9 e^{3/2}}\right )}{3 g} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {g x + f} b^{2} \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 2 \, \sqrt {g x + f} a b \log \left ({\left (e x + d\right )}^{n} c\right ) + \sqrt {g x + f} a^{2}, x\right ) \]
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 \[ \int \sqrt {g x + f} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.60, size = 0, normalized size = 0.00 \[ \int \sqrt {g x +f}\, \left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]
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 \[ \int \sqrt {f+g\,x}\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^2 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a + b \log {\left (c \left (d + e x\right )^{n} \right )}\right )^{2} \sqrt {f + g x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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