3.313 \(\int \frac{x^3}{(1+x)^{10}} \, dx\)

Optimal. Leaf size=37 \[ -\frac{1}{6 (x+1)^6}+\frac{3}{7 (x+1)^7}-\frac{3}{8 (x+1)^8}+\frac{1}{9 (x+1)^9} \]

[Out]

1/(9*(1 + x)^9) - 3/(8*(1 + x)^8) + 3/(7*(1 + x)^7) - 1/(6*(1 + x)^6)

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Rubi [A]  time = 0.0267131, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{1}{6 (x+1)^6}+\frac{3}{7 (x+1)^7}-\frac{3}{8 (x+1)^8}+\frac{1}{9 (x+1)^9} \]

Antiderivative was successfully verified.

[In]  Int[x^3/(1 + x)^10,x]

[Out]

1/(9*(1 + x)^9) - 3/(8*(1 + x)^8) + 3/(7*(1 + x)^7) - 1/(6*(1 + x)^6)

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Rubi in Sympy [A]  time = 2.15609, size = 32, normalized size = 0.86 \[ - \frac{1}{6 \left (x + 1\right )^{6}} + \frac{3}{7 \left (x + 1\right )^{7}} - \frac{3}{8 \left (x + 1\right )^{8}} + \frac{1}{9 \left (x + 1\right )^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(1+x)**10,x)

[Out]

-1/(6*(x + 1)**6) + 3/(7*(x + 1)**7) - 3/(8*(x + 1)**8) + 1/(9*(x + 1)**9)

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Mathematica [A]  time = 0.0098142, size = 24, normalized size = 0.65 \[ -\frac{84 x^3+36 x^2+9 x+1}{504 (x+1)^9} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(1 + x)^10,x]

[Out]

-(1 + 9*x + 36*x^2 + 84*x^3)/(504*(1 + x)^9)

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Maple [A]  time = 0.008, size = 30, normalized size = 0.8 \[{\frac{1}{9\, \left ( 1+x \right ) ^{9}}}-{\frac{3}{8\, \left ( 1+x \right ) ^{8}}}+{\frac{3}{7\, \left ( 1+x \right ) ^{7}}}-{\frac{1}{6\, \left ( 1+x \right ) ^{6}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(1+x)^10,x)

[Out]

1/9/(1+x)^9-3/8/(1+x)^8+3/7/(1+x)^7-1/6/(1+x)^6

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Maxima [A]  time = 1.35507, size = 84, normalized size = 2.27 \[ -\frac{84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \,{\left (x^{9} + 9 \, x^{8} + 36 \, x^{7} + 84 \, x^{6} + 126 \, x^{5} + 126 \, x^{4} + 84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x + 1)^10,x, algorithm="maxima")

[Out]

-1/504*(84*x^3 + 36*x^2 + 9*x + 1)/(x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 12
6*x^4 + 84*x^3 + 36*x^2 + 9*x + 1)

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Fricas [A]  time = 0.228135, size = 84, normalized size = 2.27 \[ -\frac{84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \,{\left (x^{9} + 9 \, x^{8} + 36 \, x^{7} + 84 \, x^{6} + 126 \, x^{5} + 126 \, x^{4} + 84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x + 1)^10,x, algorithm="fricas")

[Out]

-1/504*(84*x^3 + 36*x^2 + 9*x + 1)/(x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 12
6*x^4 + 84*x^3 + 36*x^2 + 9*x + 1)

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Sympy [A]  time = 0.198364, size = 61, normalized size = 1.65 \[ - \frac{84 x^{3} + 36 x^{2} + 9 x + 1}{504 x^{9} + 4536 x^{8} + 18144 x^{7} + 42336 x^{6} + 63504 x^{5} + 63504 x^{4} + 42336 x^{3} + 18144 x^{2} + 4536 x + 504} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(1+x)**10,x)

[Out]

-(84*x**3 + 36*x**2 + 9*x + 1)/(504*x**9 + 4536*x**8 + 18144*x**7 + 42336*x**6 +
63504*x**5 + 63504*x**4 + 42336*x**3 + 18144*x**2 + 4536*x + 504)

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GIAC/XCAS [A]  time = 0.20897, size = 30, normalized size = 0.81 \[ -\frac{84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \,{\left (x + 1\right )}^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(x + 1)^10,x, algorithm="giac")

[Out]

-1/504*(84*x^3 + 36*x^2 + 9*x + 1)/(x + 1)^9