3.1434 \(\int x^8 \left (a+b x^7\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]

[Out]

(a*x^9)/9 + (b*x^16)/16

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Rubi [A]  time = 0.0136834, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]

Antiderivative was successfully verified.

[In]  Int[x^8*(a + b*x^7),x]

[Out]

(a*x^9)/9 + (b*x^16)/16

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Rubi in Sympy [A]  time = 2.99811, size = 12, normalized size = 0.71 \[ \frac{a x^{9}}{9} + \frac{b x^{16}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**8*(b*x**7+a),x)

[Out]

a*x**9/9 + b*x**16/16

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Mathematica [A]  time = 0.00188502, size = 17, normalized size = 1. \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]

Antiderivative was successfully verified.

[In]  Integrate[x^8*(a + b*x^7),x]

[Out]

(a*x^9)/9 + (b*x^16)/16

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Maple [A]  time = 0., size = 14, normalized size = 0.8 \[{\frac{a{x}^{9}}{9}}+{\frac{b{x}^{16}}{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^8*(b*x^7+a),x)

[Out]

1/9*a*x^9+1/16*b*x^16

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Maxima [A]  time = 1.43871, size = 18, normalized size = 1.06 \[ \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)*x^8,x, algorithm="maxima")

[Out]

1/16*b*x^16 + 1/9*a*x^9

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Fricas [A]  time = 0.189639, size = 1, normalized size = 0.06 \[ \frac{1}{16} x^{16} b + \frac{1}{9} x^{9} a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)*x^8,x, algorithm="fricas")

[Out]

1/16*x^16*b + 1/9*x^9*a

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Sympy [A]  time = 0.066645, size = 12, normalized size = 0.71 \[ \frac{a x^{9}}{9} + \frac{b x^{16}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**8*(b*x**7+a),x)

[Out]

a*x**9/9 + b*x**16/16

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GIAC/XCAS [A]  time = 0.219435, size = 18, normalized size = 1.06 \[ \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)*x^8,x, algorithm="giac")

[Out]

1/16*b*x^16 + 1/9*a*x^9