\(\int (1-x^2-3 x^5) \, dx\) [1900]

Optimal result

Integrand size = 12, antiderivative size = 16 \[ \int \left (1-x^2-3 x^5\right ) \, dx=x-\frac {x^3}{3}-\frac {x^6}{2} \]

[Out]

x-1/3*x^3-1/2*x^6

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, 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 = {} \[ \int \left (1-x^2-3 x^5\right ) \, dx=-\frac {x^6}{2}-\frac {x^3}{3}+x \]

[In]

Int[1 - x^2 - 3*x^5,x]

[Out]

x - x^3/3 - x^6/2

Rubi steps \begin{align*} \text {integral}& = x-\frac {x^3}{3}-\frac {x^6}{2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \left (1-x^2-3 x^5\right ) \, dx=x-\frac {x^3}{3}-\frac {x^6}{2} \]

[In]

Integrate[1 - x^2 - 3*x^5,x]

[Out]

x - x^3/3 - x^6/2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81

method	result	size
default	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
norman	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
risch	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
parallelrisch	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
parts	\(x -\frac {1}{3} x^{3}-\frac {1}{2} x^{6}\)	\(13\)
gosper	\(-\frac {x \left (3 x^{5}+2 x^{2}-6\right )}{6}\)	\(16\)

[In]

int(-3*x^5-x^2+1,x,method=_RETURNVERBOSE)

[Out]

x-1/3*x^3-1/2*x^6

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (1-x^2-3 x^5\right ) \, dx=-\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \]

[In]

integrate(-3*x^5-x^2+1,x, algorithm="fricas")

[Out]

-1/2*x^6 - 1/3*x^3 + x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \left (1-x^2-3 x^5\right ) \, dx=- \frac {x^{6}}{2} - \frac {x^{3}}{3} + x \]

[In]

integrate(-3*x**5-x**2+1,x)

[Out]

-x**6/2 - x**3/3 + x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (1-x^2-3 x^5\right ) \, dx=-\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \]

[In]

integrate(-3*x^5-x^2+1,x, algorithm="maxima")

[Out]

-1/2*x^6 - 1/3*x^3 + x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (1-x^2-3 x^5\right ) \, dx=-\frac {1}{2} \, x^{6} - \frac {1}{3} \, x^{3} + x \]

[In]

integrate(-3*x^5-x^2+1,x, algorithm="giac")

[Out]

-1/2*x^6 - 1/3*x^3 + x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (1-x^2-3 x^5\right ) \, dx=-\frac {x^6}{2}-\frac {x^3}{3}+x \]

[In]

int(1 - 3*x^5 - x^2,x)

[Out]

x - x^3/3 - x^6/2