3.209 \(\int (a+b x^3) \, dx\)

Optimal. Leaf size=12 \[ a x+\frac{b x^4}{4} \]

[Out]

a*x + (b*x^4)/4

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Rubi [A]  time = 0.0022618, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]

Int[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

Rubi steps

\begin{align*} \int \left (a+b x^3\right ) \, dx &=a x+\frac{b x^4}{4}\\ \end{align*}

Mathematica [A]  time = 0.0000317, size = 12, normalized size = 1. \[ a x+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \begin{align*} ax+{\frac{b{x}^{4}}{4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(b*x^3+a,x)

[Out]

a*x+1/4*b*x^4

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Maxima [A]  time = 0.972193, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{4} \, b x^{4} + a x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(b*x^3+a,x, algorithm="maxima")

[Out]

1/4*b*x^4 + a*x

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Fricas [A]  time = 1.50336, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{4} x^{4} b + x a \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(b*x^3+a,x, algorithm="fricas")

[Out]

1/4*x^4*b + x*a

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Sympy [A]  time = 0.070768, size = 8, normalized size = 0.67 \begin{align*} a x + \frac{b x^{4}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(b*x**3+a,x)

[Out]

a*x + b*x**4/4

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Giac [A]  time = 1.1067, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{4} \, b x^{4} + a x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(b*x^3+a,x, algorithm="giac")

[Out]

1/4*b*x^4 + a*x