Optimal. Leaf size=964 \[ -\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \left (6 C d f a^3-b (B d f+8 C (d e+c f)) a^2+b^2 (10 c C e+3 B d e+3 B c f-4 A d f) a-b^3 (5 B c e-2 A (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left (48 C d^2 f^2 a^4-8 b d f (B d f+11 C (d e+c f)) a^3+b^2 \left (2 C \left (19 d^2 e^2+81 c d f e+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right ) a^2-b^3 \left (f (70 C e+3 B f) c^2+2 d \left (35 C e^2+11 B f e-A f^2\right ) c+d^2 e (3 B e-2 A f)\right ) a-b^4 \left (-\left (30 C e^2+5 B f e-2 A f^2\right ) c^2-d e (5 B e+2 A f) c+2 A d^2 e^2\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right ) \sqrt{e+f x}}{15 b^4 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left (24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left (15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right ) a-b^3 \left (15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 (d e-c f) \left (24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left (15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right ) a-b^3 \left (15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} \text{EllipticF}\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right ),\frac{(b c-a d) f}{d (b e-a f)}\right )}{15 b^4 \sqrt{d} (a d-b c)^{3/2} (b e-a f) \sqrt{c+d x} \sqrt{e+f x}} \]
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Rubi [A] time = 3.11586, antiderivative size = 964, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 7, integrand size = 38, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.184, Rules used = {1614, 150, 158, 114, 113, 121, 120} \[ -\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \left (6 C d f a^3-b (B d f+8 C (d e+c f)) a^2+b^2 (10 c C e+3 B d e+3 B c f-4 A d f) a-b^3 (5 B c e-2 A (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}+\frac{2 \sqrt{d} \left (48 C d^2 f^2 a^4-8 b d f (B d f+11 C (d e+c f)) a^3+b^2 \left (2 C \left (19 d^2 e^2+81 c d f e+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right ) a^2-b^3 \left (f (70 C e+3 B f) c^2+2 d \left (35 C e^2+11 B f e-A f^2\right ) c+d^2 e (3 B e-2 A f)\right ) a-b^4 \left (-\left (30 C e^2+5 B f e-2 A f^2\right ) c^2-d e (5 B e+2 A f) c+2 A d^2 e^2\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} E\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right ) \sqrt{e+f x}}{15 b^4 (a d-b c)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 \left (24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left (15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right ) a-b^3 \left (15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 (d e-c f) \left (24 C d^2 f a^3-b d (23 C d e+41 c C f+4 B d f) a^2+b^2 \left (15 C f c^2+(40 C d e+6 B d f) c+d^2 (3 B e-A f)\right ) a-b^3 \left (15 C e c^2+d (5 B e+A f) c-2 A d^2 e\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{a d-b c}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right )}{15 b^4 \sqrt{d} (a d-b c)^{3/2} (b e-a f) \sqrt{c+d x} \sqrt{e+f x}} \]
Antiderivative was successfully verified.
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Rule 1614
Rule 150
Rule 158
Rule 114
Rule 113
Rule 121
Rule 120
Rubi steps
\begin{align*} \int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{7/2}} \, dx &=-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}-\frac{2 \int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (-\frac{3 a^2 C (d e+c f)-a b (5 c C e+3 B d e+3 B c f-5 A d f)+b^2 (5 B c e-2 A (d e+c f))}{2 b}+\frac{1}{2} \left (a B d f-\frac{6 a^2 C d f}{b}+5 a C (d e+c f)-b (5 c C e+A d f)\right ) x\right )}{(a+b x)^{5/2}} \, dx}{5 (b c-a d) (b e-a f)}\\ &=\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}-\frac{4 \int \frac{\sqrt{e+f x} \left (\frac{6 a^3 C d f (d e+3 c f)-b^3 e \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (30 c^2 C e f+d^2 e (3 B e-4 A f)+c d \left (25 C e^2+6 B e f+3 A f^2\right )\right )-a^2 b \left (B d f (d e+3 c f)+C \left (8 d^2 e^2+41 c d e f+15 c^2 f^2\right )\right )}{4 b}+\frac{d \left (24 a^3 C d f^2-a^2 b f (41 C d e+23 c C f+4 B d f)-b^3 \left (15 c C e^2+A d e f+c f (5 B e-2 A f)\right )+a b^2 (5 C e (3 d e+8 c f)+f (6 B d e+3 B c f-A d f))\right ) x}{4 b}\right )}{(a+b x)^{3/2} \sqrt{c+d x}} \, dx}{15 b (b c-a d) (b e-a f)^2}\\ &=\frac{2 \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}-\frac{8 \int \frac{-\frac{24 a^4 C d^2 f^2 (d e+c f)+b^4 c e \left (15 c^2 C e f-A d^2 e f+c d \left (15 C e^2+10 B e f-A f^2\right )\right )-a b^3 \left (A d^3 e^2 f+30 c^3 C e f^2+2 c d^2 e \left (15 C e^2+7 B e f-3 A f^2\right )+c^2 d f \left (80 C e^2+14 B e f+A f^2\right )\right )-a^3 b d f \left (4 B d f (d e+c f)+C \left (41 d^2 e^2+94 c d e f+41 c^2 f^2\right )\right )+a^2 b^2 \left (C \left (15 d^3 e^3+104 c d^2 e^2 f+104 c^2 d e f^2+15 c^3 f^3\right )-d f \left (A d f (d e+c f)-2 B \left (3 d^2 e^2+7 c d e f+3 c^2 f^2\right )\right )\right )}{8 b}-\frac{d f \left (48 a^4 C d^2 f^2-8 a^3 b d f (B d f+11 C (d e+c f))-b^4 \left (2 A d^2 e^2-c d e (5 B e+2 A f)-c^2 \left (30 C e^2+5 B e f-2 A f^2\right )\right )-a b^3 \left (d^2 e (3 B e-2 A f)+c^2 f (70 C e+3 B f)+2 c d \left (35 C e^2+11 B e f-A f^2\right )\right )+a^2 b^2 \left (2 C \left (19 d^2 e^2+81 c d e f+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right )\right ) x}{8 b}}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx}{15 b^2 (b c-a d)^2 (b e-a f)^2}\\ &=\frac{2 \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{\left ((d e-c f) \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right )\right ) \int \frac{1}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx}{15 b^3 (b c-a d)^2 (b e-a f)}+\frac{\left (d \left (48 a^4 C d^2 f^2-8 a^3 b d f (B d f+11 C (d e+c f))-b^4 \left (2 A d^2 e^2-c d e (5 B e+2 A f)-c^2 \left (30 C e^2+5 B e f-2 A f^2\right )\right )-a b^3 \left (d^2 e (3 B e-2 A f)+c^2 f (70 C e+3 B f)+2 c d \left (35 C e^2+11 B e f-A f^2\right )\right )+a^2 b^2 \left (2 C \left (19 d^2 e^2+81 c d e f+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right )\right )\right ) \int \frac{\sqrt{e+f x}}{\sqrt{a+b x} \sqrt{c+d x}} \, dx}{15 b^3 (b c-a d)^2 (b e-a f)^2}\\ &=\frac{2 \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{\left ((d e-c f) \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}}\right ) \int \frac{1}{\sqrt{a+b x} \sqrt{\frac{b c}{b c-a d}+\frac{b d x}{b c-a d}} \sqrt{e+f x}} \, dx}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{c+d x}}+\frac{\left (d \left (48 a^4 C d^2 f^2-8 a^3 b d f (B d f+11 C (d e+c f))-b^4 \left (2 A d^2 e^2-c d e (5 B e+2 A f)-c^2 \left (30 C e^2+5 B e f-2 A f^2\right )\right )-a b^3 \left (d^2 e (3 B e-2 A f)+c^2 f (70 C e+3 B f)+2 c d \left (35 C e^2+11 B e f-A f^2\right )\right )+a^2 b^2 \left (2 C \left (19 d^2 e^2+81 c d e f+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x}\right ) \int \frac{\sqrt{\frac{b e}{b e-a f}+\frac{b f x}{b e-a f}}}{\sqrt{a+b x} \sqrt{\frac{b c}{b c-a d}+\frac{b d x}{b c-a d}}} \, dx}{15 b^3 (b c-a d)^2 (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}\\ &=\frac{2 \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left (48 a^4 C d^2 f^2-8 a^3 b d f (B d f+11 C (d e+c f))-b^4 \left (2 A d^2 e^2-c d e (5 B e+2 A f)-c^2 \left (30 C e^2+5 B e f-2 A f^2\right )\right )-a b^3 \left (d^2 e (3 B e-2 A f)+c^2 f (70 C e+3 B f)+2 c d \left (35 C e^2+11 B e f-A f^2\right )\right )+a^2 b^2 \left (2 C \left (19 d^2 e^2+81 c d e f+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{-b c+a d}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right )}{15 b^4 (-b c+a d)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{\left ((d e-c f) \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}}\right ) \int \frac{1}{\sqrt{a+b x} \sqrt{\frac{b c}{b c-a d}+\frac{b d x}{b c-a d}} \sqrt{\frac{b e}{b e-a f}+\frac{b f x}{b e-a f}}} \, dx}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{c+d x} \sqrt{e+f x}}\\ &=\frac{2 \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{c+d x} \sqrt{e+f x}}{15 b^3 (b c-a d)^2 (b e-a f) \sqrt{a+b x}}+\frac{2 \left (6 a^3 C d f+a b^2 (10 c C e+3 B d e+3 B c f-4 A d f)-b^3 (5 B c e-2 A (d e+c f))-a^2 b (B d f+8 C (d e+c f))\right ) \sqrt{c+d x} (e+f x)^{3/2}}{15 b^2 (b c-a d) (b e-a f)^2 (a+b x)^{3/2}}-\frac{2 \left (A b^2-a (b B-a C)\right ) (c+d x)^{3/2} (e+f x)^{3/2}}{5 b (b c-a d) (b e-a f) (a+b x)^{5/2}}+\frac{2 \sqrt{d} \left (48 a^4 C d^2 f^2-8 a^3 b d f (B d f+11 C (d e+c f))-b^4 \left (2 A d^2 e^2-c d e (5 B e+2 A f)-c^2 \left (30 C e^2+5 B e f-2 A f^2\right )\right )-a b^3 \left (d^2 e (3 B e-2 A f)+c^2 f (70 C e+3 B f)+2 c d \left (35 C e^2+11 B e f-A f^2\right )\right )+a^2 b^2 \left (2 C \left (19 d^2 e^2+81 c d e f+19 c^2 f^2\right )-d f (2 A d f-13 B (d e+c f))\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{e+f x} E\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{-b c+a d}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right )}{15 b^4 (-b c+a d)^{3/2} (b e-a f)^2 \sqrt{c+d x} \sqrt{\frac{b (e+f x)}{b e-a f}}}+\frac{2 (d e-c f) \left (24 a^3 C d^2 f-a^2 b d (23 C d e+41 c C f+4 B d f)-b^3 \left (15 c^2 C e-2 A d^2 e+c d (5 B e+A f)\right )+a b^2 \left (15 c^2 C f+d^2 (3 B e-A f)+c (40 C d e+6 B d f)\right )\right ) \sqrt{\frac{b (c+d x)}{b c-a d}} \sqrt{\frac{b (e+f x)}{b e-a f}} F\left (\sin ^{-1}\left (\frac{\sqrt{d} \sqrt{a+b x}}{\sqrt{-b c+a d}}\right )|\frac{(b c-a d) f}{d (b e-a f)}\right )}{15 b^4 \sqrt{d} (-b c+a d)^{3/2} (b e-a f) \sqrt{c+d x} \sqrt{e+f x}}\\ \end{align*}
Mathematica [C] time = 16.847, size = 9529, normalized size = 9.88 \[ \text{Result too large to show} \]
Warning: Unable to verify antiderivative.
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Maple [B] time = 0.209, size = 34395, normalized size = 35.7 \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (C x^{2} + B x + A\right )} \sqrt{d x + c} \sqrt{f x + e}}{{\left (b x + a\right )}^{\frac{7}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (C x^{2} + B x + A\right )} \sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (C x^{2} + B x + A\right )} \sqrt{d x + c} \sqrt{f x + e}}{{\left (b x + a\right )}^{\frac{7}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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