3.3.9 \(\int (a+b x^3) \, dx\) [209]

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

[Out]

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

________________________________________________________________________________________

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 = {} \begin {gather*} a x+\frac {b x^4}{4} \end {gather*}

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 = 0.00, size = 12, normalized size = 1.00 \begin {gather*} a x+\frac {b x^4}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

________________________________________________________________________________________

Maple [A]
time = 0.01, size = 11, normalized size = 0.92

method	result	size
gosper	\(a x +\frac {1}{4} b \,x^{4}\)	\(11\)
default	\(a x +\frac {1}{4} b \,x^{4}\)	\(11\)
norman	\(a x +\frac {1}{4} b \,x^{4}\)	\(11\)
risch	\(a x +\frac {1}{4} b \,x^{4}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(b*x^3+a,x,method=_RETURNVERBOSE)

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.30, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{4} \, b x^{4} + a x \end {gather*}

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

________________________________________________________________________________________

Fricas [A]
time = 0.34, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{4} \, b x^{4} + a x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*b*x^4 + a*x

________________________________________________________________________________________

Sympy [A]
time = 0.01, size = 8, normalized size = 0.67 \begin {gather*} a x + \frac {b x^{4}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x + b*x**4/4

________________________________________________________________________________________

Giac [A]
time = 1.98, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{4} \, b x^{4} + a x \end {gather*}

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

________________________________________________________________________________________

Mupad [B]
time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} \frac {b\,x^4}{4}+a\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b*x^3,x)

[Out]

a*x + (b*x^4)/4

________________________________________________________________________________________