\(\int (a+b x^4) \, dx\) [609]

Optimal result

Integrand size = 7, antiderivative size = 12 \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]

[Out]

a*x+1/5*b*x^5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, 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 = {} \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]

[In]

Int[a + b*x^4,x]

[Out]

a*x + (b*x^5)/5

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (a+b x^4\right ) \, dx=a x+\frac {b x^5}{5} \]

[In]

Integrate[a + b*x^4,x]

[Out]

a*x + (b*x^5)/5

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
gosper	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)
default	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)
norman	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)
risch	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)
parallelrisch	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)
parts	\(a x +\frac {1}{5} b \,x^{5}\)	\(11\)

[In]

int(b*x^4+a,x,method=_RETURNVERBOSE)

[Out]

a*x+1/5*b*x^5

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]

[In]

integrate(b*x^4+a,x, algorithm="fricas")

[Out]

1/5*b*x^5 + a*x

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \left (a+b x^4\right ) \, dx=a x + \frac {b x^{5}}{5} \]

[In]

integrate(b*x**4+a,x)

[Out]

a*x + b*x**5/5

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]

[In]

integrate(b*x^4+a,x, algorithm="maxima")

[Out]

1/5*b*x^5 + a*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {1}{5} \, b x^{5} + a x \]

[In]

integrate(b*x^4+a,x, algorithm="giac")

[Out]

1/5*b*x^5 + a*x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (a+b x^4\right ) \, dx=\frac {b\,x^5}{5}+a\,x \]

[In]

int(a + b*x^4,x)

[Out]

a*x + (b*x^5)/5