Optimal. Leaf size=38 \[ \frac{\left (a+b \sqrt{x}\right )^{12}}{6 b^2}-\frac{2 a \left (a+b \sqrt{x}\right )^{11}}{11 b^2} \]
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Rubi [A] time = 0.0146011, 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, Rules used = {190, 43} \[ \frac{\left (a+b \sqrt{x}\right )^{12}}{6 b^2}-\frac{2 a \left (a+b \sqrt{x}\right )^{11}}{11 b^2} \]
Antiderivative was successfully verified.
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Rule 190
Rule 43
Rubi steps
\begin{align*} \int \left (a+b \sqrt{x}\right )^{10} \, dx &=2 \operatorname{Subst}\left (\int x (a+b x)^{10} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (-\frac{a (a+b x)^{10}}{b}+\frac{(a+b x)^{11}}{b}\right ) \, dx,x,\sqrt{x}\right )\\ &=-\frac{2 a \left (a+b \sqrt{x}\right )^{11}}{11 b^2}+\frac{\left (a+b \sqrt{x}\right )^{12}}{6 b^2}\\ \end{align*}
Mathematica [A] time = 0.0267577, size = 28, normalized size = 0.74 \[ -\frac{\left (a-11 b \sqrt{x}\right ) \left (a+b \sqrt{x}\right )^{11}}{66 b^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 110, normalized size = 2.9 \begin{align*}{\frac{{x}^{6}{b}^{10}}{6}}+{\frac{20\,a{b}^{9}}{11}{x}^{{\frac{11}{2}}}}+9\,{x}^{5}{a}^{2}{b}^{8}+{\frac{80\,{a}^{3}{b}^{7}}{3}{x}^{{\frac{9}{2}}}}+{\frac{105\,{x}^{4}{a}^{4}{b}^{6}}{2}}+72\,{x}^{7/2}{a}^{5}{b}^{5}+70\,{x}^{3}{a}^{6}{b}^{4}+48\,{x}^{5/2}{a}^{7}{b}^{3}+{\frac{45\,{x}^{2}{a}^{8}{b}^{2}}{2}}+{\frac{20\,{a}^{9}b}{3}{x}^{{\frac{3}{2}}}}+x{a}^{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981726, size = 41, normalized size = 1.08 \begin{align*} \frac{{\left (b \sqrt{x} + a\right )}^{12}}{6 \, b^{2}} - \frac{2 \,{\left (b \sqrt{x} + a\right )}^{11} a}{11 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.52648, size = 259, normalized size = 6.82 \begin{align*} \frac{1}{6} \, b^{10} x^{6} + 9 \, a^{2} b^{8} x^{5} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 70 \, a^{6} b^{4} x^{3} + \frac{45}{2} \, a^{8} b^{2} x^{2} + a^{10} x + \frac{4}{33} \,{\left (15 \, a b^{9} x^{5} + 220 \, a^{3} b^{7} x^{4} + 594 \, a^{5} b^{5} x^{3} + 396 \, a^{7} b^{3} x^{2} + 55 \, a^{9} b x\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.52946, size = 133, normalized size = 3.5 \begin{align*} a^{10} x + \frac{20 a^{9} b x^{\frac{3}{2}}}{3} + \frac{45 a^{8} b^{2} x^{2}}{2} + 48 a^{7} b^{3} x^{\frac{5}{2}} + 70 a^{6} b^{4} x^{3} + 72 a^{5} b^{5} x^{\frac{7}{2}} + \frac{105 a^{4} b^{6} x^{4}}{2} + \frac{80 a^{3} b^{7} x^{\frac{9}{2}}}{3} + 9 a^{2} b^{8} x^{5} + \frac{20 a b^{9} x^{\frac{11}{2}}}{11} + \frac{b^{10} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.09573, size = 147, normalized size = 3.87 \begin{align*} \frac{1}{6} \, b^{10} x^{6} + \frac{20}{11} \, a b^{9} x^{\frac{11}{2}} + 9 \, a^{2} b^{8} x^{5} + \frac{80}{3} \, a^{3} b^{7} x^{\frac{9}{2}} + \frac{105}{2} \, a^{4} b^{6} x^{4} + 72 \, a^{5} b^{5} x^{\frac{7}{2}} + 70 \, a^{6} b^{4} x^{3} + 48 \, a^{7} b^{3} x^{\frac{5}{2}} + \frac{45}{2} \, a^{8} b^{2} x^{2} + \frac{20}{3} \, a^{9} b x^{\frac{3}{2}} + a^{10} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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