3.225 \(\int \left (b x+c x^2\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]

[Out]

(b*x^2)/2 + (c*x^3)/3

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Rubi [A]  time = 0.0120144, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]

Antiderivative was successfully verified.

[In]  Int[b*x + c*x^2,x]

[Out]

(b*x^2)/2 + (c*x^3)/3

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ b \int x\, dx + \frac{c x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(c*x**2+b*x,x)

[Out]

b*Integral(x, x) + c*x**3/3

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Mathematica [A]  time = 0.0000630367, size = 17, normalized size = 1. \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[b*x + c*x^2,x]

[Out]

(b*x^2)/2 + (c*x^3)/3

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Maple [A]  time = 0., size = 14, normalized size = 0.8 \[{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(c*x^2+b*x,x)

[Out]

1/2*b*x^2+1/3*c*x^3

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Maxima [A]  time = 0.721812, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*c*x^3 + 1/2*b*x^2

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Fricas [A]  time = 0.197897, size = 1, normalized size = 0.06 \[ \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3*c + 1/2*x^2*b

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Sympy [A]  time = 0.064842, size = 12, normalized size = 0.71 \[ \frac{b x^{2}}{2} + \frac{c x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(c*x**2+b*x,x)

[Out]

b*x**2/2 + c*x**3/3

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GIAC/XCAS [A]  time = 0.204533, size = 18, normalized size = 1.06 \[ \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*c*x^3 + 1/2*b*x^2