Optimal. Leaf size=66 \[ \frac{16 d \sqrt [4]{c+d x}}{5 \sqrt [4]{a+b x} (b c-a d)^2}-\frac{4 \sqrt [4]{c+d x}}{5 (a+b x)^{5/4} (b c-a d)} \]
[Out]
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Rubi [A] time = 0.0505276, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{16 d \sqrt [4]{c+d x}}{5 \sqrt [4]{a+b x} (b c-a d)^2}-\frac{4 \sqrt [4]{c+d x}}{5 (a+b x)^{5/4} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(9/4)*(c + d*x)^(3/4)),x]
[Out]
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Rubi in Sympy [A] time = 6.78994, size = 56, normalized size = 0.85 \[ \frac{16 d \sqrt [4]{c + d x}}{5 \sqrt [4]{a + b x} \left (a d - b c\right )^{2}} + \frac{4 \sqrt [4]{c + d x}}{5 \left (a + b x\right )^{\frac{5}{4}} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(9/4)/(d*x+c)**(3/4),x)
[Out]
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Mathematica [A] time = 0.0628399, size = 46, normalized size = 0.7 \[ \frac{4 \sqrt [4]{c+d x} (5 a d-b c+4 b d x)}{5 (a+b x)^{5/4} (b c-a d)^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(9/4)*(c + d*x)^(3/4)),x]
[Out]
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Maple [A] time = 0.009, size = 54, normalized size = 0.8 \[{\frac{16\,bdx+20\,ad-4\,bc}{5\,{a}^{2}{d}^{2}-10\,abcd+5\,{b}^{2}{c}^{2}}\sqrt [4]{dx+c} \left ( bx+a \right ) ^{-{\frac{5}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(9/4)/(d*x+c)^(3/4),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{9}{4}}{\left (d x + c\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(9/4)*(d*x + c)^(3/4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225615, size = 159, normalized size = 2.41 \[ \frac{4 \,{\left (4 \, b d x - b c + 5 \, a d\right )}{\left (b x + a\right )}^{\frac{3}{4}}{\left (d x + c\right )}^{\frac{1}{4}}}{5 \,{\left (a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} +{\left (b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right )} x^{2} + 2 \,{\left (a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right )} x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(9/4)*(d*x + c)^(3/4)),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)**(9/4)/(d*x+c)**(3/4),x)
[Out]
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GIAC/XCAS [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)^(9/4)*(d*x + c)^(3/4)),x, algorithm="giac")
[Out]