\(\int (-x^3+x^4) \, dx\) [1892]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int \left (-x^3+x^4\right ) \, dx=-\frac {x^4}{4}+\frac {x^5}{5} \]

[Out]

-1/4*x^4+1/5*x^5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, 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 = {} \[ \int \left (-x^3+x^4\right ) \, dx=\frac {x^5}{5}-\frac {x^4}{4} \]

[In]

Int[-x^3 + x^4,x]

[Out]

-1/4*x^4 + x^5/5

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \left (-x^3+x^4\right ) \, dx=-\frac {x^4}{4}+\frac {x^5}{5} \]

[In]

Integrate[-x^3 + x^4,x]

[Out]

-1/4*x^4 + x^5/5

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73

method	result	size
gosper	\(\frac {x^{4} \left (-5+4 x \right )}{20}\)	\(11\)
default	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
norman	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
risch	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
parallelrisch	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)
parts	\(-\frac {1}{4} x^{4}+\frac {1}{5} x^{5}\)	\(12\)

[In]

int(x^4-x^3,x,method=_RETURNVERBOSE)

[Out]

1/20*x^4*(-5+4*x)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-x^3+x^4\right ) \, dx=\frac {1}{5} \, x^{5} - \frac {1}{4} \, x^{4} \]

[In]

integrate(x^4-x^3,x, algorithm="fricas")

[Out]

1/5*x^5 - 1/4*x^4

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \left (-x^3+x^4\right ) \, dx=\frac {x^{5}}{5} - \frac {x^{4}}{4} \]

[In]

integrate(x**4-x**3,x)

[Out]

x**5/5 - x**4/4

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-x^3+x^4\right ) \, dx=\frac {1}{5} \, x^{5} - \frac {1}{4} \, x^{4} \]

[In]

integrate(x^4-x^3,x, algorithm="maxima")

[Out]

1/5*x^5 - 1/4*x^4

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-x^3+x^4\right ) \, dx=\frac {1}{5} \, x^{5} - \frac {1}{4} \, x^{4} \]

[In]

integrate(x^4-x^3,x, algorithm="giac")

[Out]

1/5*x^5 - 1/4*x^4

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \left (-x^3+x^4\right ) \, dx=\frac {x^4\,\left (4\,x-5\right )}{20} \]

[In]

int(x^4 - x^3,x)

[Out]

(x^4*(4*x - 5))/20