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

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

[Out]

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

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \[ a x+\frac {b x^4}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

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fricas [A]  time = 0.50, size = 10, normalized size = 0.83 \[ \frac {1}{4} x^{4} b + x a \]

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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giac [A]  time = 0.15, size = 10, normalized size = 0.83 \[ \frac {1}{4} \, b x^{4} + a x \]

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

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maple [A]  time = 0.00, size = 11, normalized size = 0.92 \[ \frac {1}{4} b \,x^{4}+a x \]

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 = 1.32, size = 10, normalized size = 0.83 \[ \frac {1}{4} \, b x^{4} + a x \]

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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mupad [B]  time = 0.02, size = 10, normalized size = 0.83 \[ \frac {b\,x^4}{4}+a\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b*x^3,x)

[Out]

a*x + (b*x^4)/4

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sympy [A]  time = 0.09, size = 8, normalized size = 0.67 \[ a x + \frac {b x^{4}}{4} \]

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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