Optimal. Leaf size=38 \[ \frac{2 \left (a+b \sqrt{x}\right )^7}{7 b^2}-\frac{a \left (a+b \sqrt{x}\right )^6}{3 b^2} \]
[Out]
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Rubi [A] time = 0.0450174, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{2 \left (a+b \sqrt{x}\right )^7}{7 b^2}-\frac{a \left (a+b \sqrt{x}\right )^6}{3 b^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^5,x]
[Out]
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Rubi in Sympy [A] time = 8.07235, size = 32, normalized size = 0.84 \[ - \frac{a \left (a + b \sqrt{x}\right )^{6}}{3 b^{2}} + \frac{2 \left (a + b \sqrt{x}\right )^{7}}{7 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**5,x)
[Out]
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Mathematica [A] time = 0.0127571, size = 66, normalized size = 1.74 \[ a^5 x+\frac{10}{3} a^4 b x^{3/2}+5 a^3 b^2 x^2+4 a^2 b^3 x^{5/2}+\frac{5}{3} a b^4 x^3+\frac{2}{7} b^5 x^{7/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^5,x]
[Out]
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Maple [A] time = 0.003, size = 55, normalized size = 1.5 \[{\frac{2\,{b}^{5}}{7}{x}^{{\frac{7}{2}}}}+{\frac{5\,a{b}^{4}{x}^{3}}{3}}+4\,{a}^{2}{b}^{3}{x}^{5/2}+5\,{a}^{3}{b}^{2}{x}^{2}+{\frac{10\,{a}^{4}b}{3}{x}^{{\frac{3}{2}}}}+x{a}^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^5,x)
[Out]
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Maxima [A] time = 1.43983, size = 73, normalized size = 1.92 \[ \frac{2}{7} \, b^{5} x^{\frac{7}{2}} + \frac{5}{3} \, a b^{4} x^{3} + 4 \, a^{2} b^{3} x^{\frac{5}{2}} + 5 \, a^{3} b^{2} x^{2} + \frac{10}{3} \, a^{4} b x^{\frac{3}{2}} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229263, size = 78, normalized size = 2.05 \[ \frac{5}{3} \, a b^{4} x^{3} + 5 \, a^{3} b^{2} x^{2} + a^{5} x + \frac{2}{21} \,{\left (3 \, b^{5} x^{3} + 42 \, a^{2} b^{3} x^{2} + 35 \, a^{4} b x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.43243, size = 66, normalized size = 1.74 \[ a^{5} x + \frac{10 a^{4} b x^{\frac{3}{2}}}{3} + 5 a^{3} b^{2} x^{2} + 4 a^{2} b^{3} x^{\frac{5}{2}} + \frac{5 a b^{4} x^{3}}{3} + \frac{2 b^{5} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**5,x)
[Out]
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GIAC/XCAS [A] time = 0.213633, size = 73, normalized size = 1.92 \[ \frac{2}{7} \, b^{5} x^{\frac{7}{2}} + \frac{5}{3} \, a b^{4} x^{3} + 4 \, a^{2} b^{3} x^{\frac{5}{2}} + 5 \, a^{3} b^{2} x^{2} + \frac{10}{3} \, a^{4} b x^{\frac{3}{2}} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^5,x, algorithm="giac")
[Out]