3.1282 \(\int (c+d x)^7 \, dx\)

Optimal. Leaf size=14 \[ \frac{(c+d x)^8}{8 d} \]

[Out]

(c + d*x)^8/(8*d)

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Rubi [A]  time = 0.00710682, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{(c+d x)^8}{8 d} \]

Antiderivative was successfully verified.

[In]  Int[(c + d*x)^7,x]

[Out]

(c + d*x)^8/(8*d)

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Rubi in Sympy [A]  time = 1.29931, size = 8, normalized size = 0.57 \[ \frac{\left (c + d x\right )^{8}}{8 d} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((d*x+c)**7,x)

[Out]

(c + d*x)**8/(8*d)

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Mathematica [A]  time = 0.00147576, size = 14, normalized size = 1. \[ \frac{(c+d x)^8}{8 d} \]

Antiderivative was successfully verified.

[In]  Integrate[(c + d*x)^7,x]

[Out]

(c + d*x)^8/(8*d)

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Maple [A]  time = 0., size = 13, normalized size = 0.9 \[{\frac{ \left ( dx+c \right ) ^{8}}{8\,d}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((d*x+c)^7,x)

[Out]

1/8*(d*x+c)^8/d

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Maxima [A]  time = 1.33371, size = 16, normalized size = 1.14 \[ \frac{{\left (d x + c\right )}^{8}}{8 \, d} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^7,x, algorithm="maxima")

[Out]

1/8*(d*x + c)^8/d

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Fricas [A]  time = 0.177554, size = 1, normalized size = 0.07 \[ \frac{1}{8} x^{8} d^{7} + x^{7} d^{6} c + \frac{7}{2} x^{6} d^{5} c^{2} + 7 x^{5} d^{4} c^{3} + \frac{35}{4} x^{4} d^{3} c^{4} + 7 x^{3} d^{2} c^{5} + \frac{7}{2} x^{2} d c^{6} + x c^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^7,x, algorithm="fricas")

[Out]

1/8*x^8*d^7 + x^7*d^6*c + 7/2*x^6*d^5*c^2 + 7*x^5*d^4*c^3 + 35/4*x^4*d^3*c^4 + 7
*x^3*d^2*c^5 + 7/2*x^2*d*c^6 + x*c^7

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Sympy [A]  time = 0.114348, size = 83, normalized size = 5.93 \[ c^{7} x + \frac{7 c^{6} d x^{2}}{2} + 7 c^{5} d^{2} x^{3} + \frac{35 c^{4} d^{3} x^{4}}{4} + 7 c^{3} d^{4} x^{5} + \frac{7 c^{2} d^{5} x^{6}}{2} + c d^{6} x^{7} + \frac{d^{7} x^{8}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x+c)**7,x)

[Out]

c**7*x + 7*c**6*d*x**2/2 + 7*c**5*d**2*x**3 + 35*c**4*d**3*x**4/4 + 7*c**3*d**4*
x**5 + 7*c**2*d**5*x**6/2 + c*d**6*x**7 + d**7*x**8/8

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GIAC/XCAS [A]  time = 0.216408, size = 16, normalized size = 1.14 \[ \frac{{\left (d x + c\right )}^{8}}{8 \, d} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^7,x, algorithm="giac")

[Out]

1/8*(d*x + c)^8/d