### 3.225 $$\int (b x+c x^2) \, dx$$

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 = 0.00323, 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., Rules used = {} $\frac{b x^2}{2}+\frac{c x^3}{3}$

Antiderivative was successfully veriﬁed.

[In]

Int[b*x + c*x^2,x]

[Out]

(b*x^2)/2 + (c*x^3)/3

Rubi steps

\begin{align*} \int \left (b x+c x^2\right ) \, dx &=\frac{b x^2}{2}+\frac{c x^3}{3}\\ \end{align*}

Mathematica [A]  time = 0.0000396, 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 = 0.043, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \end{align*}

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 = 1.15944, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \end{align*}

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 = 1.3568, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b \end{align*}

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 = 0.15272, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{2}}{2} + \frac{c x^{3}}{3} \end{align*}

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 [A]  time = 1.28656, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \end{align*}

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