Optimal. Leaf size=134 \[ -\frac{7776 b^2 d (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^4}-\frac{1296 b d (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^3}-\frac{108 d (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)^2}-\frac{6}{\sqrt [6]{a+b x} (c+d x)^{17/6} (b c-a d)} \]
[Out]
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Rubi [A] time = 0.124579, antiderivative size = 134, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{7776 b^2 d (a+b x)^{5/6}}{935 (c+d x)^{5/6} (b c-a d)^4}-\frac{1296 b d (a+b x)^{5/6}}{187 (c+d x)^{11/6} (b c-a d)^3}-\frac{108 d (a+b x)^{5/6}}{17 (c+d x)^{17/6} (b c-a d)^2}-\frac{6}{\sqrt [6]{a+b x} (c+d x)^{17/6} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(7/6)*(c + d*x)^(23/6)),x]
[Out]
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Rubi in Sympy [A] time = 19.3749, size = 121, normalized size = 0.9 \[ - \frac{7776 b^{2} d \left (a + b x\right )^{\frac{5}{6}}}{935 \left (c + d x\right )^{\frac{5}{6}} \left (a d - b c\right )^{4}} + \frac{1296 b d \left (a + b x\right )^{\frac{5}{6}}}{187 \left (c + d x\right )^{\frac{11}{6}} \left (a d - b c\right )^{3}} - \frac{108 d \left (a + b x\right )^{\frac{5}{6}}}{17 \left (c + d x\right )^{\frac{17}{6}} \left (a d - b c\right )^{2}} + \frac{6}{\sqrt [6]{a + b x} \left (c + d x\right )^{\frac{17}{6}} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(7/6)/(d*x+c)**(23/6),x)
[Out]
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Mathematica [A] time = 0.234569, size = 97, normalized size = 0.72 \[ \frac{6 (a+b x)^{5/6} \sqrt [6]{c+d x} \left (-\frac{935 b^3}{a+b x}-\frac{145 b d (b c-a d)}{(c+d x)^2}-\frac{55 d (b c-a d)^2}{(c+d x)^3}-\frac{361 b^2 d}{c+d x}\right )}{935 (b c-a d)^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(23/6)),x]
[Out]
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Maple [A] time = 0.013, size = 171, normalized size = 1.3 \[ -{\frac{7776\,{x}^{3}{b}^{3}{d}^{3}+1296\,a{b}^{2}{d}^{3}{x}^{2}+22032\,{b}^{3}c{d}^{2}{x}^{2}-540\,{a}^{2}b{d}^{3}x+3672\,a{b}^{2}c{d}^{2}x+20196\,{b}^{3}{c}^{2}dx+330\,{a}^{3}{d}^{3}-1530\,{a}^{2}cb{d}^{2}+3366\,a{b}^{2}{c}^{2}d+5610\,{b}^{3}{c}^{3}}{935\,{a}^{4}{d}^{4}-3740\,{a}^{3}bc{d}^{3}+5610\,{a}^{2}{c}^{2}{b}^{2}{d}^{2}-3740\,a{b}^{3}{c}^{3}d+935\,{b}^{4}{c}^{4}}{\frac{1}{\sqrt [6]{bx+a}}} \left ( dx+c \right ) ^{-{\frac{17}{6}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(7/6)/(d*x+c)^(23/6),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{23}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(23/6)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222684, size = 393, normalized size = 2.93 \[ -\frac{6 \,{\left (1296 \, b^{3} d^{3} x^{3} + 935 \, b^{3} c^{3} + 561 \, a b^{2} c^{2} d - 255 \, a^{2} b c d^{2} + 55 \, a^{3} d^{3} + 216 \,{\left (17 \, b^{3} c d^{2} + a b^{2} d^{3}\right )} x^{2} + 18 \,{\left (187 \, b^{3} c^{2} d + 34 \, a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right )} x\right )}}{935 \,{\left (b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4} +{\left (b^{4} c^{4} d^{2} - 4 \, a b^{3} c^{3} d^{3} + 6 \, a^{2} b^{2} c^{2} d^{4} - 4 \, a^{3} b c d^{5} + a^{4} d^{6}\right )} x^{2} + 2 \,{\left (b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3} - 4 \, a^{3} b c^{2} d^{4} + a^{4} c d^{5}\right )} x\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{5}{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(23/6)),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**(7/6)/(d*x+c)**(23/6),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{23}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(23/6)),x, algorithm="giac")
[Out]