Optimal. Leaf size=84 \[ -\frac{4 a^3 \sqrt{a+b \sqrt{x}}}{b^4}+\frac{4 a^2 \left (a+b \sqrt{x}\right )^{3/2}}{b^4}+\frac{4 \left (a+b \sqrt{x}\right )^{7/2}}{7 b^4}-\frac{12 a \left (a+b \sqrt{x}\right )^{5/2}}{5 b^4} \]
[Out]
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Rubi [A] time = 0.0978998, antiderivative size = 84, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{4 a^3 \sqrt{a+b \sqrt{x}}}{b^4}+\frac{4 a^2 \left (a+b \sqrt{x}\right )^{3/2}}{b^4}+\frac{4 \left (a+b \sqrt{x}\right )^{7/2}}{7 b^4}-\frac{12 a \left (a+b \sqrt{x}\right )^{5/2}}{5 b^4} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[a + b*Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 14.4778, size = 78, normalized size = 0.93 \[ - \frac{4 a^{3} \sqrt{a + b \sqrt{x}}}{b^{4}} + \frac{4 a^{2} \left (a + b \sqrt{x}\right )^{\frac{3}{2}}}{b^{4}} - \frac{12 a \left (a + b \sqrt{x}\right )^{\frac{5}{2}}}{5 b^{4}} + \frac{4 \left (a + b \sqrt{x}\right )^{\frac{7}{2}}}{7 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(a+b*x**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0279793, size = 54, normalized size = 0.64 \[ \frac{4 \sqrt{a+b \sqrt{x}} \left (-16 a^3+8 a^2 b \sqrt{x}-6 a b^2 x+5 b^3 x^{3/2}\right )}{35 b^4} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[a + b*Sqrt[x]],x]
[Out]
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Maple [A] time = 0.003, size = 57, normalized size = 0.7 \[ 4\,{\frac{1/7\, \left ( a+b\sqrt{x} \right ) ^{7/2}-3/5\,a \left ( a+b\sqrt{x} \right ) ^{5/2}+ \left ( a+b\sqrt{x} \right ) ^{3/2}{a}^{2}-\sqrt{a+b\sqrt{x}}{a}^{3}}{{b}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(a+b*x^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 1.43805, size = 86, normalized size = 1.02 \[ \frac{4 \,{\left (b \sqrt{x} + a\right )}^{\frac{7}{2}}}{7 \, b^{4}} - \frac{12 \,{\left (b \sqrt{x} + a\right )}^{\frac{5}{2}} a}{5 \, b^{4}} + \frac{4 \,{\left (b \sqrt{x} + a\right )}^{\frac{3}{2}} a^{2}}{b^{4}} - \frac{4 \, \sqrt{b \sqrt{x} + a} a^{3}}{b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(b*sqrt(x) + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24437, size = 61, normalized size = 0.73 \[ -\frac{4 \,{\left (6 \, a b^{2} x + 16 \, a^{3} -{\left (5 \, b^{3} x + 8 \, a^{2} b\right )} \sqrt{x}\right )} \sqrt{b \sqrt{x} + a}}{35 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(b*sqrt(x) + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.66146, size = 1872, normalized size = 22.29 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a+b*x**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.3005, size = 77, normalized size = 0.92 \[ \frac{4 \,{\left (5 \,{\left (b \sqrt{x} + a\right )}^{\frac{7}{2}} - 21 \,{\left (b \sqrt{x} + a\right )}^{\frac{5}{2}} a + 35 \,{\left (b \sqrt{x} + a\right )}^{\frac{3}{2}} a^{2} - 35 \, \sqrt{b \sqrt{x} + a} a^{3}\right )}}{35 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(b*sqrt(x) + a),x, algorithm="giac")
[Out]