\(\int (4 x+\pi x^3) \, dx\) [1895]

Optimal result

Integrand size = 9, antiderivative size = 14 \[ \int \left (4 x+\pi x^3\right ) \, dx=2 x^2+\frac {\pi x^4}{4} \]

[Out]

2*x^2+1/4*Pi*x^4

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {\pi x^4}{4}+2 x^2 \]

[In]

Int[4*x + Pi*x^3,x]

[Out]

2*x^2 + (Pi*x^4)/4

Rubi steps \begin{align*} \text {integral}& = 2 x^2+\frac {\pi x^4}{4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (4 x+\pi x^3\right ) \, dx=2 x^2+\frac {\pi x^4}{4} \]

[In]

Integrate[4*x + Pi*x^3,x]

[Out]

2*x^2 + (Pi*x^4)/4

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93

method	result	size
gosper	\(\frac {x^{2} \left (\pi \,x^{2}+8\right )}{4}\)	\(13\)
norman	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
risch	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
parallelrisch	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
parts	\(2 x^{2}+\frac {1}{4} \pi \,x^{4}\)	\(13\)
default	\(\frac {\left (\pi \,x^{2}+4\right )^{2}}{4 \pi }\)	\(15\)

[In]

int(Pi*x^3+4*x,x,method=_RETURNVERBOSE)

[Out]

1/4*x^2*(Pi*x^2+8)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \]

[In]

integrate(pi*x^3+4*x,x, algorithm="fricas")

[Out]

1/4*pi*x^4 + 2*x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {\pi x^{4}}{4} + 2 x^{2} \]

[In]

integrate(pi*x**3+4*x,x)

[Out]

pi*x**4/4 + 2*x**2

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \]

[In]

integrate(pi*x^3+4*x,x, algorithm="maxima")

[Out]

1/4*pi*x^4 + 2*x^2

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {1}{4} \, \pi x^{4} + 2 \, x^{2} \]

[In]

integrate(pi*x^3+4*x,x, algorithm="giac")

[Out]

1/4*pi*x^4 + 2*x^2

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (4 x+\pi x^3\right ) \, dx=\frac {\Pi \,x^4}{4}+2\,x^2 \]

[In]

int(4*x + Pi*x^3,x)

[Out]

(Pi*x^4)/4 + 2*x^2