Optimal. Leaf size=46 \[ \frac{2 \left (a-b 2^x\right )^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a-b 2^x}}{b^2 \log (2)} \]
[Out]
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Rubi [A] time = 0.078743, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{2 \left (a-b 2^x\right )^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a-b 2^x}}{b^2 \log (2)} \]
Antiderivative was successfully verified.
[In] Int[4^x/Sqrt[a - 2^x*b],x]
[Out]
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Rubi in Sympy [A] time = 10.0612, size = 39, normalized size = 0.85 \[ - \frac{2 a \sqrt{- 2^{x} b + a}}{b^{2} \log{\left (2 \right )}} + \frac{2 \left (- 2^{x} b + a\right )^{\frac{3}{2}}}{3 b^{2} \log{\left (2 \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(4**x/(a-2**x*b)**(1/2),x)
[Out]
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Mathematica [A] time = 0.10092, size = 57, normalized size = 1.24 \[ \frac{2 \left (2 a^2 \left (\sqrt{1-\frac{b 2^x}{a}}-1\right )+a b 2^x+b^2 4^x\right )}{b^2 \log (8) \sqrt{a-b 2^x}} \]
Antiderivative was successfully verified.
[In] Integrate[4^x/Sqrt[a - 2^x*b],x]
[Out]
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Maple [A] time = 0.024, size = 29, normalized size = 0.6 \[ -{\frac{2\,{2}^{x}b+4\,a}{3\,{b}^{2}\ln \left ( 2 \right ) }\sqrt{a-{2}^{x}b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(4^x/(a-2^x*b)^(1/2),x)
[Out]
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Maxima [A] time = 0.902818, size = 96, normalized size = 2.09 \[ \frac{2^{2 \, x + 1}}{3 \, \sqrt{-2^{x} b + a} \log \left (2\right )} + \frac{2^{x + 1} a}{3 \, \sqrt{-2^{x} b + a} b \log \left (2\right )} - \frac{4 \, a^{2}}{3 \, \sqrt{-2^{x} b + a} b^{2} \log \left (2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4^x/sqrt(-2^x*b + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243144, size = 38, normalized size = 0.83 \[ -\frac{2 \,{\left (2^{x} b + 2 \, a\right )} \sqrt{-2^{x} b + a}}{3 \, b^{2} \log \left (2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4^x/sqrt(-2^x*b + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.62732, size = 58, normalized size = 1.26 \[ \begin{cases} - \frac{2 \cdot 2^{x} \sqrt{- 2^{x} b + a}}{3 b \log{\left (2 \right )}} - \frac{4 a \sqrt{- 2^{x} b + a}}{3 b^{2} \log{\left (2 \right )}} & \text{for}\: b \neq 0 \\\frac{4^{x}}{2 \sqrt{a} \log{\left (2 \right )}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4**x/(a-2**x*b)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{4^{x}}{\sqrt{-2^{x} b + a}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4^x/sqrt(-2^x*b + a),x, algorithm="giac")
[Out]