Optimal. Leaf size=46 \[ \frac {b \left (a+b \sqrt {x}\right )^{11}}{66 a^2 x^{11/2}}-\frac {\left (a+b \sqrt {x}\right )^{11}}{6 a x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {266, 45, 37} \[ \frac {b \left (a+b \sqrt {x}\right )^{11}}{66 a^2 x^{11/2}}-\frac {\left (a+b \sqrt {x}\right )^{11}}{6 a x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 45
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt {x}\right )^{10}}{x^7} \, dx &=2 \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{13}} \, dx,x,\sqrt {x}\right )\\ &=-\frac {\left (a+b \sqrt {x}\right )^{11}}{6 a x^6}-\frac {b \operatorname {Subst}\left (\int \frac {(a+b x)^{10}}{x^{12}} \, dx,x,\sqrt {x}\right )}{6 a}\\ &=-\frac {\left (a+b \sqrt {x}\right )^{11}}{6 a x^6}+\frac {b \left (a+b \sqrt {x}\right )^{11}}{66 a^2 x^{11/2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 32, normalized size = 0.70 \[ \frac {\left (b \sqrt {x}-11 a\right ) \left (a+b \sqrt {x}\right )^{11}}{66 a^2 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.20, size = 113, normalized size = 2.46 \[ -\frac {66 \, b^{10} x^{5} + 1485 \, a^{2} b^{8} x^{4} + 4620 \, a^{4} b^{6} x^{3} + 3465 \, a^{6} b^{4} x^{2} + 594 \, a^{8} b^{2} x + 11 \, a^{10} + 8 \, {\left (55 \, a b^{9} x^{4} + 396 \, a^{3} b^{7} x^{3} + 594 \, a^{5} b^{5} x^{2} + 220 \, a^{7} b^{3} x + 15 \, a^{9} b\right )} \sqrt {x}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.16, size = 112, normalized size = 2.43 \[ -\frac {66 \, b^{10} x^{5} + 440 \, a b^{9} x^{\frac {9}{2}} + 1485 \, a^{2} b^{8} x^{4} + 3168 \, a^{3} b^{7} x^{\frac {7}{2}} + 4620 \, a^{4} b^{6} x^{3} + 4752 \, a^{5} b^{5} x^{\frac {5}{2}} + 3465 \, a^{6} b^{4} x^{2} + 1760 \, a^{7} b^{3} x^{\frac {3}{2}} + 594 \, a^{8} b^{2} x + 120 \, a^{9} b \sqrt {x} + 11 \, a^{10}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 113, normalized size = 2.46 \[ -\frac {b^{10}}{x}-\frac {20 a \,b^{9}}{3 x^{\frac {3}{2}}}-\frac {45 a^{2} b^{8}}{2 x^{2}}-\frac {48 a^{3} b^{7}}{x^{\frac {5}{2}}}-\frac {70 a^{4} b^{6}}{x^{3}}-\frac {72 a^{5} b^{5}}{x^{\frac {7}{2}}}-\frac {105 a^{6} b^{4}}{2 x^{4}}-\frac {80 a^{7} b^{3}}{3 x^{\frac {9}{2}}}-\frac {9 a^{8} b^{2}}{x^{5}}-\frac {20 a^{9} b}{11 x^{\frac {11}{2}}}-\frac {a^{10}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.91, size = 112, normalized size = 2.43 \[ -\frac {66 \, b^{10} x^{5} + 440 \, a b^{9} x^{\frac {9}{2}} + 1485 \, a^{2} b^{8} x^{4} + 3168 \, a^{3} b^{7} x^{\frac {7}{2}} + 4620 \, a^{4} b^{6} x^{3} + 4752 \, a^{5} b^{5} x^{\frac {5}{2}} + 3465 \, a^{6} b^{4} x^{2} + 1760 \, a^{7} b^{3} x^{\frac {3}{2}} + 594 \, a^{8} b^{2} x + 120 \, a^{9} b \sqrt {x} + 11 \, a^{10}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.13, size = 111, normalized size = 2.41 \[ -\frac {\frac {a^{10}}{6}+b^{10}\,x^5+9\,a^8\,b^2\,x+\frac {20\,a^9\,b\,\sqrt {x}}{11}+\frac {20\,a\,b^9\,x^{9/2}}{3}+\frac {105\,a^6\,b^4\,x^2}{2}+70\,a^4\,b^6\,x^3+\frac {45\,a^2\,b^8\,x^4}{2}+\frac {80\,a^7\,b^3\,x^{3/2}}{3}+72\,a^5\,b^5\,x^{5/2}+48\,a^3\,b^7\,x^{7/2}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 3.64, size = 134, normalized size = 2.91 \[ - \frac {a^{10}}{6 x^{6}} - \frac {20 a^{9} b}{11 x^{\frac {11}{2}}} - \frac {9 a^{8} b^{2}}{x^{5}} - \frac {80 a^{7} b^{3}}{3 x^{\frac {9}{2}}} - \frac {105 a^{6} b^{4}}{2 x^{4}} - \frac {72 a^{5} b^{5}}{x^{\frac {7}{2}}} - \frac {70 a^{4} b^{6}}{x^{3}} - \frac {48 a^{3} b^{7}}{x^{\frac {5}{2}}} - \frac {45 a^{2} b^{8}}{2 x^{2}} - \frac {20 a b^{9}}{3 x^{\frac {3}{2}}} - \frac {b^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________