\(\int (-1-60 x+900 x^3) \, dx\) [8657]

Optimal result

Integrand size = 10, antiderivative size = 16 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=-3-x+\left (-1+15 x^2\right )^2+\log (9) \]

[Out]

(15*x^2-1)^2+2*ln(3)-3-x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-1-60 x+900 x^3\right ) \, dx=225 x^4-30 x^2-x \]

[In]

Int[-1 - 60*x + 900*x^3,x]

[Out]

-x - 30*x^2 + 225*x^4

Rubi steps \begin{align*} \text {integral}& = -x-30 x^2+225 x^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=-x-30 x^2+225 x^4 \]

[In]

Integrate[-1 - 60*x + 900*x^3,x]

[Out]

-x - 30*x^2 + 225*x^4

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94

method	result	size
gosper	\(225 x^{4}-30 x^{2}-x\)	\(15\)
default	\(225 x^{4}-30 x^{2}-x\)	\(15\)
norman	\(225 x^{4}-30 x^{2}-x\)	\(15\)
risch	\(225 x^{4}-30 x^{2}-x\)	\(15\)
parallelrisch	\(225 x^{4}-30 x^{2}-x\)	\(15\)
parts	\(225 x^{4}-30 x^{2}-x\)	\(15\)

[In]

int(900*x^3-60*x-1,x,method=_RETURNVERBOSE)

[Out]

225*x^4-30*x^2-x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=225 \, x^{4} - 30 \, x^{2} - x \]

[In]

integrate(900*x^3-60*x-1,x, algorithm="fricas")

[Out]

225*x^4 - 30*x^2 - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=225 x^{4} - 30 x^{2} - x \]

[In]

integrate(900*x**3-60*x-1,x)

[Out]

225*x**4 - 30*x**2 - x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=225 \, x^{4} - 30 \, x^{2} - x \]

[In]

integrate(900*x^3-60*x-1,x, algorithm="maxima")

[Out]

225*x^4 - 30*x^2 - x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=225 \, x^{4} - 30 \, x^{2} - x \]

[In]

integrate(900*x^3-60*x-1,x, algorithm="giac")

[Out]

225*x^4 - 30*x^2 - x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \left (-1-60 x+900 x^3\right ) \, dx=-x\,\left (-225\,x^3+30\,x+1\right ) \]

[In]

int(900*x^3 - 60*x - 1,x)

[Out]

-x*(30*x - 225*x^3 + 1)