3.2.36 \(\int (b x^2+c x^4) \, dx\) [136]

Optimal. Leaf size=17 \[ \frac {b x^3}{3}+\frac {c x^5}{5} \]

[Out]

1/3*b*x^3+1/5*c*x^5

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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {b x^3}{3}+\frac {c x^5}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[b*x^2 + c*x^4,x]

[Out]

(b*x^3)/3 + (c*x^5)/5

Rubi steps

\begin {align*} \int \left (b x^2+c x^4\right ) \, dx &=\frac {b x^3}{3}+\frac {c x^5}{5}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {b x^3}{3}+\frac {c x^5}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[b*x^2 + c*x^4,x]

[Out]

(b*x^3)/3 + (c*x^5)/5

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Maple [A]
time = 0.02, size = 14, normalized size = 0.82

method	result	size
default	\(\frac {1}{3} b \,x^{3}+\frac {1}{5} c \,x^{5}\)	\(14\)
norman	\(\frac {1}{3} b \,x^{3}+\frac {1}{5} c \,x^{5}\)	\(14\)
risch	\(\frac {1}{3} b \,x^{3}+\frac {1}{5} c \,x^{5}\)	\(14\)
gosper	\(\frac {x^{3} \left (3 c \,x^{2}+5 b \right )}{15}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(c*x^4+b*x^2,x,method=_RETURNVERBOSE)

[Out]

1/3*b*x^3+1/5*c*x^5

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Maxima [A]
time = 0.28, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{3} \, b x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(c*x^4+b*x^2,x, algorithm="maxima")

[Out]

1/5*c*x^5 + 1/3*b*x^3

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Fricas [A]
time = 0.34, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{3} \, b x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(c*x^4+b*x^2,x, algorithm="fricas")

[Out]

1/5*c*x^5 + 1/3*b*x^3

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Sympy [A]
time = 0.01, size = 12, normalized size = 0.71 \begin {gather*} \frac {b x^{3}}{3} + \frac {c x^{5}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(c*x**4+b*x**2,x)

[Out]

b*x**3/3 + c*x**5/5

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Giac [A]
time = 3.97, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{3} \, b x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(c*x^4+b*x^2,x, algorithm="giac")

[Out]

1/5*c*x^5 + 1/3*b*x^3

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Mupad [B]
time = 0.02, size = 13, normalized size = 0.76 \begin {gather*} \frac {c\,x^5}{5}+\frac {b\,x^3}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(b*x^2 + c*x^4,x)

[Out]

(b*x^3)/3 + (c*x^5)/5

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