3.271 \(\int \frac{\left (a+b x^3\right )^5}{x^{22}} \, dx\)

Optimal. Leaf size=40 \[ \frac{b \left (a+b x^3\right )^6}{126 a^2 x^{18}}-\frac{\left (a+b x^3\right )^6}{21 a x^{21}} \]

[Out]

-(a + b*x^3)^6/(21*a*x^21) + (b*(a + b*x^3)^6)/(126*a^2*x^18)

_______________________________________________________________________________________

Rubi [A]  time = 0.0521835, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^3\right )^6}{126 a^2 x^{18}}-\frac{\left (a+b x^3\right )^6}{21 a x^{21}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^5/x^22,x]

[Out]

-(a + b*x^3)^6/(21*a*x^21) + (b*(a + b*x^3)^6)/(126*a^2*x^18)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 5.79237, size = 32, normalized size = 0.8 \[ - \frac{\left (a + b x^{3}\right )^{6}}{21 a x^{21}} + \frac{b \left (a + b x^{3}\right )^{6}}{126 a^{2} x^{18}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**5/x**22,x)

[Out]

-(a + b*x**3)**6/(21*a*x**21) + b*(a + b*x**3)**6/(126*a**2*x**18)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00747992, size = 69, normalized size = 1.72 \[ -\frac{a^5}{21 x^{21}}-\frac{5 a^4 b}{18 x^{18}}-\frac{2 a^3 b^2}{3 x^{15}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^5/x^22,x]

[Out]

-a^5/(21*x^21) - (5*a^4*b)/(18*x^18) - (2*a^3*b^2)/(3*x^15) - (5*a^2*b^3)/(6*x^1
2) - (5*a*b^4)/(9*x^9) - b^5/(6*x^6)

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 58, normalized size = 1.5 \[ -{\frac{5\,{a}^{2}{b}^{3}}{6\,{x}^{12}}}-{\frac{2\,{a}^{3}{b}^{2}}{3\,{x}^{15}}}-{\frac{5\,{a}^{4}b}{18\,{x}^{18}}}-{\frac{{b}^{5}}{6\,{x}^{6}}}-{\frac{{a}^{5}}{21\,{x}^{21}}}-{\frac{5\,a{b}^{4}}{9\,{x}^{9}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^5/x^22,x)

[Out]

-5/6*a^2*b^3/x^12-2/3*a^3*b^2/x^15-5/18*a^4*b/x^18-1/6*b^5/x^6-1/21*a^5/x^21-5/9
*a*b^4/x^9

_______________________________________________________________________________________

Maxima [A]  time = 1.44937, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^22,x, algorithm="maxima")

[Out]

-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*
b*x^3 + 6*a^5)/x^21

_______________________________________________________________________________________

Fricas [A]  time = 0.209432, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^22,x, algorithm="fricas")

[Out]

-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*
b*x^3 + 6*a^5)/x^21

_______________________________________________________________________________________

Sympy [A]  time = 3.07306, size = 63, normalized size = 1.58 \[ - \frac{6 a^{5} + 35 a^{4} b x^{3} + 84 a^{3} b^{2} x^{6} + 105 a^{2} b^{3} x^{9} + 70 a b^{4} x^{12} + 21 b^{5} x^{15}}{126 x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**5/x**22,x)

[Out]

-(6*a**5 + 35*a**4*b*x**3 + 84*a**3*b**2*x**6 + 105*a**2*b**3*x**9 + 70*a*b**4*x
**12 + 21*b**5*x**15)/(126*x**21)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.225787, size = 80, normalized size = 2. \[ -\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^5/x^22,x, algorithm="giac")

[Out]

-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*
b*x^3 + 6*a^5)/x^21