\(\int (5+2 x+3 x^2+4 x^3) \, dx\) [1901]

Optimal result

Integrand size = 15, antiderivative size = 13 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=5 x+x^2+x^3+x^4 \]

[Out]

x^4+x^3+x^2+5*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, 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 = {} \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^4+x^3+x^2+5 x \]

[In]

Int[5 + 2*x + 3*x^2 + 4*x^3,x]

[Out]

5*x + x^2 + x^3 + x^4

Rubi steps \begin{align*} \text {integral}& = 5 x+x^2+x^3+x^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=5 x+x^2+x^3+x^4 \]

[In]

Integrate[5 + 2*x + 3*x^2 + 4*x^3,x]

[Out]

5*x + x^2 + x^3 + x^4

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08

method	result	size
gosper	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
default	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
norman	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
risch	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
parallelrisch	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
parts	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)

[In]

int(4*x^3+3*x^2+2*x+5,x,method=_RETURNVERBOSE)

[Out]

x^4+x^3+x^2+5*x

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^{4} + x^{3} + x^{2} + 5 \, x \]

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="fricas")

[Out]

x^4 + x^3 + x^2 + 5*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^{4} + x^{3} + x^{2} + 5 x \]

[In]

integrate(4*x**3+3*x**2+2*x+5,x)

[Out]

x**4 + x**3 + x**2 + 5*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^{4} + x^{3} + x^{2} + 5 \, x \]

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="maxima")

[Out]

x^4 + x^3 + x^2 + 5*x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^{4} + x^{3} + x^{2} + 5 \, x \]

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="giac")

[Out]

x^4 + x^3 + x^2 + 5*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx=x^4+x^3+x^2+5\,x \]

[In]

int(2*x + 3*x^2 + 4*x^3 + 5,x)

[Out]

5*x + x^2 + x^3 + x^4