3.136 \(\int (b x^2+c x^4) \, dx\)

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

[Out]

(b*x^3)/3 + (c*x^5)/5

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Rubi [A]  time = 0.0030681, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{b x^3}{3}+\frac{c x^5}{5} \]

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*}

Mathematica [A]  time = 0.000033, size = 17, normalized size = 1. \[ \frac{b x^3}{3}+\frac{c x^5}{5} \]

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 = 0.042, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{3}}{3}}+{\frac{c{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0.955986, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} \end{align*}

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 = 1.09512, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{5} x^{5} c + \frac{1}{3} x^{3} b \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*x^5*c + 1/3*x^3*b

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Sympy [A]  time = 0.074365, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{3}}{3} + \frac{c x^{5}}{5} \end{align*}

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 = 1.21641, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} \end{align*}

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