Optimal. Leaf size=287 \[ -\frac {2 (e f-d g)^3 \left (c f^2-b f g+a g^2\right ) \sqrt {f+g x}}{g^6}+\frac {2 (e f-d g)^2 (c f (5 e f-2 d g)-g (4 b e f-b d g-3 a e g)) (f+g x)^{3/2}}{3 g^6}+\frac {2 (e f-d g) \left (3 e g (2 b e f-b d g-a e g)-c \left (10 e^2 f^2-8 d e f g+d^2 g^2\right )\right ) (f+g x)^{5/2}}{5 g^6}-\frac {2 e \left (e g (4 b e f-3 b d g-a e g)-c \left (10 e^2 f^2-12 d e f g+3 d^2 g^2\right )\right ) (f+g x)^{7/2}}{7 g^6}-\frac {2 e^2 (5 c e f-3 c d g-b e g) (f+g x)^{9/2}}{9 g^6}+\frac {2 c e^3 (f+g x)^{11/2}}{11 g^6} \]
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Rubi [A]
time = 0.32, antiderivative size = 287, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {911, 1167}
\begin {gather*} -\frac {2 e (f+g x)^{7/2} \left (e g (-a e g-3 b d g+4 b e f)-c \left (3 d^2 g^2-12 d e f g+10 e^2 f^2\right )\right )}{7 g^6}+\frac {2 (f+g x)^{5/2} (e f-d g) \left (3 e g (-a e g-b d g+2 b e f)-c \left (d^2 g^2-8 d e f g+10 e^2 f^2\right )\right )}{5 g^6}-\frac {2 \sqrt {f+g x} (e f-d g)^3 \left (a g^2-b f g+c f^2\right )}{g^6}+\frac {2 (f+g x)^{3/2} (e f-d g)^2 (c f (5 e f-2 d g)-g (-3 a e g-b d g+4 b e f))}{3 g^6}-\frac {2 e^2 (f+g x)^{9/2} (-b e g-3 c d g+5 c e f)}{9 g^6}+\frac {2 c e^3 (f+g x)^{11/2}}{11 g^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 911
Rule 1167
Rubi steps
\begin {align*} \int \frac {(d+e x)^3 \left (a+b x+c x^2\right )}{\sqrt {f+g x}} \, dx &=\frac {2 \text {Subst}\left (\int \left (\frac {-e f+d g}{g}+\frac {e x^2}{g}\right )^3 \left (\frac {c f^2-b f g+a g^2}{g^2}-\frac {(2 c f-b g) x^2}{g^2}+\frac {c x^4}{g^2}\right ) \, dx,x,\sqrt {f+g x}\right )}{g}\\ &=\frac {2 \text {Subst}\left (\int \left (\frac {(-e f+d g)^3 \left (c f^2-b f g+a g^2\right )}{g^5}+\frac {(e f-d g)^2 (c f (5 e f-2 d g)-g (4 b e f-b d g-3 a e g)) x^2}{g^5}+\frac {(e f-d g) \left (3 e g (2 b e f-b d g-a e g)-c \left (10 e^2 f^2-8 d e f g+d^2 g^2\right )\right ) x^4}{g^5}+\frac {e \left (-e g (4 b e f-3 b d g-a e g)+c \left (10 e^2 f^2-12 d e f g+3 d^2 g^2\right )\right ) x^6}{g^5}+\frac {e^2 (-5 c e f+3 c d g+b e g) x^8}{g^5}+\frac {c e^3 x^{10}}{g^5}\right ) \, dx,x,\sqrt {f+g x}\right )}{g}\\ &=-\frac {2 (e f-d g)^3 \left (c f^2-b f g+a g^2\right ) \sqrt {f+g x}}{g^6}+\frac {2 (e f-d g)^2 (c f (5 e f-2 d g)-g (4 b e f-b d g-3 a e g)) (f+g x)^{3/2}}{3 g^6}+\frac {2 (e f-d g) \left (3 e g (2 b e f-b d g-a e g)-c \left (10 e^2 f^2-8 d e f g+d^2 g^2\right )\right ) (f+g x)^{5/2}}{5 g^6}-\frac {2 e \left (e g (4 b e f-3 b d g-a e g)-c \left (10 e^2 f^2-12 d e f g+3 d^2 g^2\right )\right ) (f+g x)^{7/2}}{7 g^6}-\frac {2 e^2 (5 c e f-3 c d g-b e g) (f+g x)^{9/2}}{9 g^6}+\frac {2 c e^3 (f+g x)^{11/2}}{11 g^6}\\ \end {align*}
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Mathematica [A]
time = 0.32, size = 412, normalized size = 1.44 \begin {gather*} \frac {2 \sqrt {f+g x} \left (c \left (231 d^3 g^3 \left (8 f^2-4 f g x+3 g^2 x^2\right )+297 d^2 e g^2 \left (-16 f^3+8 f^2 g x-6 f g^2 x^2+5 g^3 x^3\right )+33 d e^2 g \left (128 f^4-64 f^3 g x+48 f^2 g^2 x^2-40 f g^3 x^3+35 g^4 x^4\right )-5 e^3 \left (256 f^5-128 f^4 g x+96 f^3 g^2 x^2-80 f^2 g^3 x^3+70 f g^4 x^4-63 g^5 x^5\right )\right )+11 g \left (9 a g \left (35 d^3 g^3+35 d^2 e g^2 (-2 f+g x)+7 d e^2 g \left (8 f^2-4 f g x+3 g^2 x^2\right )+e^3 \left (-16 f^3+8 f^2 g x-6 f g^2 x^2+5 g^3 x^3\right )\right )+b \left (105 d^3 g^3 (-2 f+g x)+63 d^2 e g^2 \left (8 f^2-4 f g x+3 g^2 x^2\right )+27 d e^2 g \left (-16 f^3+8 f^2 g x-6 f g^2 x^2+5 g^3 x^3\right )+e^3 \left (128 f^4-64 f^3 g x+48 f^2 g^2 x^2-40 f g^3 x^3+35 g^4 x^4\right )\right )\right )\right )}{3465 g^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 285, normalized size = 0.99 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 411, normalized size = 1.43 \begin {gather*} \frac {2 \, {\left (315 \, {\left (g x + f\right )}^{\frac {11}{2}} c e^{3} - 385 \, {\left (5 \, c f e^{3} - {\left (3 \, c d e^{2} + b e^{3}\right )} g\right )} {\left (g x + f\right )}^{\frac {9}{2}} + 495 \, {\left (10 \, c f^{2} e^{3} - 4 \, {\left (3 \, c d e^{2} + b e^{3}\right )} f g + {\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} g^{2}\right )} {\left (g x + f\right )}^{\frac {7}{2}} - 693 \, {\left (10 \, c f^{3} e^{3} - 6 \, {\left (3 \, c d e^{2} + b e^{3}\right )} f^{2} g + 3 \, {\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} f g^{2} - {\left (c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right )} g^{3}\right )} {\left (g x + f\right )}^{\frac {5}{2}} + 1155 \, {\left (5 \, c f^{4} e^{3} - 4 \, {\left (3 \, c d e^{2} + b e^{3}\right )} f^{3} g + 3 \, {\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} f^{2} g^{2} - 2 \, {\left (c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right )} f g^{3} + {\left (b d^{3} + 3 \, a d^{2} e\right )} g^{4}\right )} {\left (g x + f\right )}^{\frac {3}{2}} + 3465 \, {\left (a d^{3} g^{5} - c f^{5} e^{3} + {\left (3 \, c d e^{2} + b e^{3}\right )} f^{4} g - {\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} f^{3} g^{2} + {\left (c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right )} f^{2} g^{3} - {\left (b d^{3} + 3 \, a d^{2} e\right )} f g^{4}\right )} \sqrt {g x + f}\right )}}{3465 \, g^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.19, size = 458, normalized size = 1.60 \begin {gather*} \frac {2 \, {\left (693 \, c d^{3} g^{5} x^{2} + 1848 \, c d^{3} f^{2} g^{3} - 2310 \, b d^{3} f g^{4} + 3465 \, a d^{3} g^{5} - 231 \, {\left (4 \, c d^{3} f g^{4} - 5 \, b d^{3} g^{5}\right )} x + {\left (315 \, c g^{5} x^{5} - 1280 \, c f^{5} + 1408 \, b f^{4} g - 1584 \, a f^{3} g^{2} - 35 \, {\left (10 \, c f g^{4} - 11 \, b g^{5}\right )} x^{4} + 5 \, {\left (80 \, c f^{2} g^{3} - 88 \, b f g^{4} + 99 \, a g^{5}\right )} x^{3} - 6 \, {\left (80 \, c f^{3} g^{2} - 88 \, b f^{2} g^{3} + 99 \, a f g^{4}\right )} x^{2} + 8 \, {\left (80 \, c f^{4} g - 88 \, b f^{3} g^{2} + 99 \, a f^{2} g^{3}\right )} x\right )} e^{3} + 33 \, {\left (35 \, c d g^{5} x^{4} + 128 \, c d f^{4} g - 144 \, b d f^{3} g^{2} + 168 \, a d f^{2} g^{3} - 5 \, {\left (8 \, c d f g^{4} - 9 \, b d g^{5}\right )} x^{3} + 3 \, {\left (16 \, c d f^{2} g^{3} - 18 \, b d f g^{4} + 21 \, a d g^{5}\right )} x^{2} - 4 \, {\left (16 \, c d f^{3} g^{2} - 18 \, b d f^{2} g^{3} + 21 \, a d f g^{4}\right )} x\right )} e^{2} + 99 \, {\left (15 \, c d^{2} g^{5} x^{3} - 48 \, c d^{2} f^{3} g^{2} + 56 \, b d^{2} f^{2} g^{3} - 70 \, a d^{2} f g^{4} - 3 \, {\left (6 \, c d^{2} f g^{4} - 7 \, b d^{2} g^{5}\right )} x^{2} + {\left (24 \, c d^{2} f^{2} g^{3} - 28 \, b d^{2} f g^{4} + 35 \, a d^{2} g^{5}\right )} x\right )} e\right )} \sqrt {g x + f}}{3465 \, g^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1544 vs.
\(2 (291) = 582\).
time = 73.95, size = 1544, normalized size = 5.38 \begin {gather*} \begin {cases} \frac {- \frac {2 a d^{3} f}{\sqrt {f + g x}} - 2 a d^{3} \left (- \frac {f}{\sqrt {f + g x}} - \sqrt {f + g x}\right ) - \frac {6 a d^{2} e f \left (- \frac {f}{\sqrt {f + g x}} - \sqrt {f + g x}\right )}{g} - \frac {6 a d^{2} e \left (\frac {f^{2}}{\sqrt {f + g x}} + 2 f \sqrt {f + g x} - \frac {\left (f + g x\right )^{\frac {3}{2}}}{3}\right )}{g} - \frac {6 a d e^{2} f \left (\frac {f^{2}}{\sqrt {f + g x}} + 2 f \sqrt {f + g x} - \frac {\left (f + g x\right )^{\frac {3}{2}}}{3}\right )}{g^{2}} - \frac {6 a d e^{2} \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{2}} - \frac {2 a e^{3} f \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{3}} - \frac {2 a e^{3} \left (\frac {f^{4}}{\sqrt {f + g x}} + 4 f^{3} \sqrt {f + g x} - 2 f^{2} \left (f + g x\right )^{\frac {3}{2}} + \frac {4 f \left (f + g x\right )^{\frac {5}{2}}}{5} - \frac {\left (f + g x\right )^{\frac {7}{2}}}{7}\right )}{g^{3}} - \frac {2 b d^{3} f \left (- \frac {f}{\sqrt {f + g x}} - \sqrt {f + g x}\right )}{g} - \frac {2 b d^{3} \left (\frac {f^{2}}{\sqrt {f + g x}} + 2 f \sqrt {f + g x} - \frac {\left (f + g x\right )^{\frac {3}{2}}}{3}\right )}{g} - \frac {6 b d^{2} e f \left (\frac {f^{2}}{\sqrt {f + g x}} + 2 f \sqrt {f + g x} - \frac {\left (f + g x\right )^{\frac {3}{2}}}{3}\right )}{g^{2}} - \frac {6 b d^{2} e \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{2}} - \frac {6 b d e^{2} f \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{3}} - \frac {6 b d e^{2} \left (\frac {f^{4}}{\sqrt {f + g x}} + 4 f^{3} \sqrt {f + g x} - 2 f^{2} \left (f + g x\right )^{\frac {3}{2}} + \frac {4 f \left (f + g x\right )^{\frac {5}{2}}}{5} - \frac {\left (f + g x\right )^{\frac {7}{2}}}{7}\right )}{g^{3}} - \frac {2 b e^{3} f \left (\frac {f^{4}}{\sqrt {f + g x}} + 4 f^{3} \sqrt {f + g x} - 2 f^{2} \left (f + g x\right )^{\frac {3}{2}} + \frac {4 f \left (f + g x\right )^{\frac {5}{2}}}{5} - \frac {\left (f + g x\right )^{\frac {7}{2}}}{7}\right )}{g^{4}} - \frac {2 b e^{3} \left (- \frac {f^{5}}{\sqrt {f + g x}} - 5 f^{4} \sqrt {f + g x} + \frac {10 f^{3} \left (f + g x\right )^{\frac {3}{2}}}{3} - 2 f^{2} \left (f + g x\right )^{\frac {5}{2}} + \frac {5 f \left (f + g x\right )^{\frac {7}{2}}}{7} - \frac {\left (f + g x\right )^{\frac {9}{2}}}{9}\right )}{g^{4}} - \frac {2 c d^{3} f \left (\frac {f^{2}}{\sqrt {f + g x}} + 2 f \sqrt {f + g x} - \frac {\left (f + g x\right )^{\frac {3}{2}}}{3}\right )}{g^{2}} - \frac {2 c d^{3} \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{2}} - \frac {6 c d^{2} e f \left (- \frac {f^{3}}{\sqrt {f + g x}} - 3 f^{2} \sqrt {f + g x} + f \left (f + g x\right )^{\frac {3}{2}} - \frac {\left (f + g x\right )^{\frac {5}{2}}}{5}\right )}{g^{3}} - \frac {6 c d^{2} e \left (\frac {f^{4}}{\sqrt {f + g x}} + 4 f^{3} \sqrt {f + g x} - 2 f^{2} \left (f + g x\right )^{\frac {3}{2}} + \frac {4 f \left (f + g x\right )^{\frac {5}{2}}}{5} - \frac {\left (f + g x\right )^{\frac {7}{2}}}{7}\right )}{g^{3}} - \frac {6 c d e^{2} f \left (\frac {f^{4}}{\sqrt {f + g x}} + 4 f^{3} \sqrt {f + g x} - 2 f^{2} \left (f + g x\right )^{\frac {3}{2}} + \frac {4 f \left (f + g x\right )^{\frac {5}{2}}}{5} - \frac {\left (f + g x\right )^{\frac {7}{2}}}{7}\right )}{g^{4}} - \frac {6 c d e^{2} \left (- \frac {f^{5}}{\sqrt {f + g x}} - 5 f^{4} \sqrt {f + g x} + \frac {10 f^{3} \left (f + g x\right )^{\frac {3}{2}}}{3} - 2 f^{2} \left (f + g x\right )^{\frac {5}{2}} + \frac {5 f \left (f + g x\right )^{\frac {7}{2}}}{7} - \frac {\left (f + g x\right )^{\frac {9}{2}}}{9}\right )}{g^{4}} - \frac {2 c e^{3} f \left (- \frac {f^{5}}{\sqrt {f + g x}} - 5 f^{4} \sqrt {f + g x} + \frac {10 f^{3} \left (f + g x\right )^{\frac {3}{2}}}{3} - 2 f^{2} \left (f + g x\right )^{\frac {5}{2}} + \frac {5 f \left (f + g x\right )^{\frac {7}{2}}}{7} - \frac {\left (f + g x\right )^{\frac {9}{2}}}{9}\right )}{g^{5}} - \frac {2 c e^{3} \left (\frac {f^{6}}{\sqrt {f + g x}} + 6 f^{5} \sqrt {f + g x} - 5 f^{4} \left (f + g x\right )^{\frac {3}{2}} + 4 f^{3} \left (f + g x\right )^{\frac {5}{2}} - \frac {15 f^{2} \left (f + g x\right )^{\frac {7}{2}}}{7} + \frac {2 f \left (f + g x\right )^{\frac {9}{2}}}{3} - \frac {\left (f + g x\right )^{\frac {11}{2}}}{11}\right )}{g^{5}}}{g} & \text {for}\: g \neq 0 \\\frac {a d^{3} x + \frac {c e^{3} x^{6}}{6} + \frac {x^{5} \left (b e^{3} + 3 c d e^{2}\right )}{5} + \frac {x^{4} \left (a e^{3} + 3 b d e^{2} + 3 c d^{2} e\right )}{4} + \frac {x^{3} \cdot \left (3 a d e^{2} + 3 b d^{2} e + c d^{3}\right )}{3} + \frac {x^{2} \cdot \left (3 a d^{2} e + b d^{3}\right )}{2}}{\sqrt {f}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 565 vs.
\(2 (271) = 542\).
time = 4.32, size = 565, normalized size = 1.97 \begin {gather*} \frac {2 \, {\left (3465 \, \sqrt {g x + f} a d^{3} + \frac {1155 \, {\left ({\left (g x + f\right )}^{\frac {3}{2}} - 3 \, \sqrt {g x + f} f\right )} b d^{3}}{g} + \frac {3465 \, {\left ({\left (g x + f\right )}^{\frac {3}{2}} - 3 \, \sqrt {g x + f} f\right )} a d^{2} e}{g} + \frac {231 \, {\left (3 \, {\left (g x + f\right )}^{\frac {5}{2}} - 10 \, {\left (g x + f\right )}^{\frac {3}{2}} f + 15 \, \sqrt {g x + f} f^{2}\right )} c d^{3}}{g^{2}} + \frac {693 \, {\left (3 \, {\left (g x + f\right )}^{\frac {5}{2}} - 10 \, {\left (g x + f\right )}^{\frac {3}{2}} f + 15 \, \sqrt {g x + f} f^{2}\right )} b d^{2} e}{g^{2}} + \frac {693 \, {\left (3 \, {\left (g x + f\right )}^{\frac {5}{2}} - 10 \, {\left (g x + f\right )}^{\frac {3}{2}} f + 15 \, \sqrt {g x + f} f^{2}\right )} a d e^{2}}{g^{2}} + \frac {297 \, {\left (5 \, {\left (g x + f\right )}^{\frac {7}{2}} - 21 \, {\left (g x + f\right )}^{\frac {5}{2}} f + 35 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{2} - 35 \, \sqrt {g x + f} f^{3}\right )} c d^{2} e}{g^{3}} + \frac {297 \, {\left (5 \, {\left (g x + f\right )}^{\frac {7}{2}} - 21 \, {\left (g x + f\right )}^{\frac {5}{2}} f + 35 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{2} - 35 \, \sqrt {g x + f} f^{3}\right )} b d e^{2}}{g^{3}} + \frac {99 \, {\left (5 \, {\left (g x + f\right )}^{\frac {7}{2}} - 21 \, {\left (g x + f\right )}^{\frac {5}{2}} f + 35 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{2} - 35 \, \sqrt {g x + f} f^{3}\right )} a e^{3}}{g^{3}} + \frac {33 \, {\left (35 \, {\left (g x + f\right )}^{\frac {9}{2}} - 180 \, {\left (g x + f\right )}^{\frac {7}{2}} f + 378 \, {\left (g x + f\right )}^{\frac {5}{2}} f^{2} - 420 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{3} + 315 \, \sqrt {g x + f} f^{4}\right )} c d e^{2}}{g^{4}} + \frac {11 \, {\left (35 \, {\left (g x + f\right )}^{\frac {9}{2}} - 180 \, {\left (g x + f\right )}^{\frac {7}{2}} f + 378 \, {\left (g x + f\right )}^{\frac {5}{2}} f^{2} - 420 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{3} + 315 \, \sqrt {g x + f} f^{4}\right )} b e^{3}}{g^{4}} + \frac {5 \, {\left (63 \, {\left (g x + f\right )}^{\frac {11}{2}} - 385 \, {\left (g x + f\right )}^{\frac {9}{2}} f + 990 \, {\left (g x + f\right )}^{\frac {7}{2}} f^{2} - 1386 \, {\left (g x + f\right )}^{\frac {5}{2}} f^{3} + 1155 \, {\left (g x + f\right )}^{\frac {3}{2}} f^{4} - 693 \, \sqrt {g x + f} f^{5}\right )} c e^{3}}{g^{5}}\right )}}{3465 \, g} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 283, normalized size = 0.99 \begin {gather*} \frac {{\left (f+g\,x\right )}^{9/2}\,\left (2\,b\,e^3\,g-10\,c\,e^3\,f+6\,c\,d\,e^2\,g\right )}{9\,g^6}+\frac {{\left (f+g\,x\right )}^{7/2}\,\left (6\,c\,d^2\,e\,g^2-24\,c\,d\,e^2\,f\,g+6\,b\,d\,e^2\,g^2+20\,c\,e^3\,f^2-8\,b\,e^3\,f\,g+2\,a\,e^3\,g^2\right )}{7\,g^6}+\frac {2\,{\left (f+g\,x\right )}^{5/2}\,\left (d\,g-e\,f\right )\,\left (c\,d^2\,g^2-8\,c\,d\,e\,f\,g+3\,b\,d\,e\,g^2+10\,c\,e^2\,f^2-6\,b\,e^2\,f\,g+3\,a\,e^2\,g^2\right )}{5\,g^6}+\frac {2\,\sqrt {f+g\,x}\,{\left (d\,g-e\,f\right )}^3\,\left (c\,f^2-b\,f\,g+a\,g^2\right )}{g^6}+\frac {2\,{\left (f+g\,x\right )}^{3/2}\,{\left (d\,g-e\,f\right )}^2\,\left (3\,a\,e\,g^2+b\,d\,g^2+5\,c\,e\,f^2-4\,b\,e\,f\,g-2\,c\,d\,f\,g\right )}{3\,g^6}+\frac {2\,c\,e^3\,{\left (f+g\,x\right )}^{11/2}}{11\,g^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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