3.316 \(\int (a+b x)^{9/2} \, dx\)

Optimal. Leaf size=16 \[ \frac{2 (a+b x)^{11/2}}{11 b} \]

[Out]

(2*(a + b*x)^(11/2))/(11*b)

_______________________________________________________________________________________

Rubi [A]  time = 0.00695355, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{2 (a+b x)^{11/2}}{11 b} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^(9/2),x]

[Out]

(2*(a + b*x)^(11/2))/(11*b)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.26444, size = 12, normalized size = 0.75 \[ \frac{2 \left (a + b x\right )^{\frac{11}{2}}}{11 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**(9/2),x)

[Out]

2*(a + b*x)**(11/2)/(11*b)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0102769, size = 16, normalized size = 1. \[ \frac{2 (a+b x)^{11/2}}{11 b} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^(9/2),x]

[Out]

(2*(a + b*x)^(11/2))/(11*b)

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[{\frac{2}{11\,b} \left ( bx+a \right ) ^{{\frac{11}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^(9/2),x)

[Out]

2/11*(b*x+a)^(11/2)/b

_______________________________________________________________________________________

Maxima [A]  time = 1.32456, size = 16, normalized size = 1. \[ \frac{2 \,{\left (b x + a\right )}^{\frac{11}{2}}}{11 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^(9/2),x, algorithm="maxima")

[Out]

2/11*(b*x + a)^(11/2)/b

_______________________________________________________________________________________

Fricas [A]  time = 0.209376, size = 82, normalized size = 5.12 \[ \frac{2 \,{\left (b^{5} x^{5} + 5 \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x^{3} + 10 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5}\right )} \sqrt{b x + a}}{11 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^(9/2),x, algorithm="fricas")

[Out]

2/11*(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5)
*sqrt(b*x + a)/b

_______________________________________________________________________________________

Sympy [A]  time = 0.102526, size = 12, normalized size = 0.75 \[ \frac{2 \left (a + b x\right )^{\frac{11}{2}}}{11 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**(9/2),x)

[Out]

2*(a + b*x)**(11/2)/(11*b)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210457, size = 309, normalized size = 19.31 \[ \frac{2 \,{\left (1155 \,{\left (b x + a\right )}^{\frac{3}{2}} a^{4} + 924 \,{\left (3 \,{\left (b x + a\right )}^{\frac{5}{2}} - 5 \,{\left (b x + a\right )}^{\frac{3}{2}} a\right )} a^{3} + \frac{198 \,{\left (15 \,{\left (b x + a\right )}^{\frac{7}{2}} b^{12} - 42 \,{\left (b x + a\right )}^{\frac{5}{2}} a b^{12} + 35 \,{\left (b x + a\right )}^{\frac{3}{2}} a^{2} b^{12}\right )} a^{2}}{b^{12}} + \frac{44 \,{\left (35 \,{\left (b x + a\right )}^{\frac{9}{2}} b^{24} - 135 \,{\left (b x + a\right )}^{\frac{7}{2}} a b^{24} + 189 \,{\left (b x + a\right )}^{\frac{5}{2}} a^{2} b^{24} - 105 \,{\left (b x + a\right )}^{\frac{3}{2}} a^{3} b^{24}\right )} a}{b^{24}} + \frac{315 \,{\left (b x + a\right )}^{\frac{11}{2}} b^{40} - 1540 \,{\left (b x + a\right )}^{\frac{9}{2}} a b^{40} + 2970 \,{\left (b x + a\right )}^{\frac{7}{2}} a^{2} b^{40} - 2772 \,{\left (b x + a\right )}^{\frac{5}{2}} a^{3} b^{40} + 1155 \,{\left (b x + a\right )}^{\frac{3}{2}} a^{4} b^{40}}{b^{40}}\right )}}{3465 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^(9/2),x, algorithm="giac")

[Out]

2/3465*(1155*(b*x + a)^(3/2)*a^4 + 924*(3*(b*x + a)^(5/2) - 5*(b*x + a)^(3/2)*a)
*a^3 + 198*(15*(b*x + a)^(7/2)*b^12 - 42*(b*x + a)^(5/2)*a*b^12 + 35*(b*x + a)^(
3/2)*a^2*b^12)*a^2/b^12 + 44*(35*(b*x + a)^(9/2)*b^24 - 135*(b*x + a)^(7/2)*a*b^
24 + 189*(b*x + a)^(5/2)*a^2*b^24 - 105*(b*x + a)^(3/2)*a^3*b^24)*a/b^24 + (315*
(b*x + a)^(11/2)*b^40 - 1540*(b*x + a)^(9/2)*a*b^40 + 2970*(b*x + a)^(7/2)*a^2*b
^40 - 2772*(b*x + a)^(5/2)*a^3*b^40 + 1155*(b*x + a)^(3/2)*a^4*b^40)/b^40)/b