Optimal. Leaf size=42 \[ \frac{4 \left (a+b \sqrt{x}\right )^{5/2}}{5 b^2}-\frac{4 a \left (a+b \sqrt{x}\right )^{3/2}}{3 b^2} \]
[Out]
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Rubi [A] time = 0.0474007, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{4 \left (a+b \sqrt{x}\right )^{5/2}}{5 b^2}-\frac{4 a \left (a+b \sqrt{x}\right )^{3/2}}{3 b^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 6.04349, size = 37, normalized size = 0.88 \[ - \frac{4 a \left (a + b \sqrt{x}\right )^{\frac{3}{2}}}{3 b^{2}} + \frac{4 \left (a + b \sqrt{x}\right )^{\frac{5}{2}}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0193036, size = 40, normalized size = 0.95 \[ \frac{4 \sqrt{a+b \sqrt{x}} \left (-2 a^2+a b \sqrt{x}+3 b^2 x\right )}{15 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b*Sqrt[x]],x]
[Out]
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Maple [A] time = 0.004, size = 30, normalized size = 0.7 \[ 4\,{\frac{1/5\, \left ( a+b\sqrt{x} \right ) ^{5/2}-1/3\, \left ( a+b\sqrt{x} \right ) ^{3/2}a}{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^(1/2),x)
[Out]
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Maxima [A] time = 1.45126, size = 41, normalized size = 0.98 \[ \frac{4 \,{\left (b \sqrt{x} + a\right )}^{\frac{5}{2}}}{5 \, b^{2}} - \frac{4 \,{\left (b \sqrt{x} + a\right )}^{\frac{3}{2}} a}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*sqrt(x) + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24716, size = 43, normalized size = 1.02 \[ \frac{4 \,{\left (3 \, b^{2} x + a b \sqrt{x} - 2 \, a^{2}\right )} \sqrt{b \sqrt{x} + a}}{15 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*sqrt(x) + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.9724, size = 272, normalized size = 6.48 \[ - \frac{8 a^{\frac{9}{2}} x^{2} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{9}{2}} x^{2}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} - \frac{4 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{8 a^{\frac{7}{2}} b x^{\frac{5}{2}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{16 a^{\frac{5}{2}} b^{2} x^{3} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} + \frac{12 a^{\frac{3}{2}} b^{3} x^{\frac{7}{2}} \sqrt{1 + \frac{b \sqrt{x}}{a}}}{15 a^{2} b^{2} x^{2} + 15 a b^{3} x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.251155, size = 39, normalized size = 0.93 \[ \frac{4 \,{\left (3 \,{\left (b \sqrt{x} + a\right )}^{\frac{5}{2}} - 5 \,{\left (b \sqrt{x} + a\right )}^{\frac{3}{2}} a\right )}}{15 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*sqrt(x) + a),x, algorithm="giac")
[Out]