3.54 \(\int (1+4 x+4 x^2+4 x^4) \, dx\)

Optimal. Leaf size=21 \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]

[Out]

x+2*x^2+4/3*x^3+4/5*x^5

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Rubi [A]  time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]

Int[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

Rubi steps

\begin {align*} \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx &=x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 21, normalized size = 1.00 \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]

Integrate[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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fricas [A]  time = 0.34, size = 17, normalized size = 0.81 \[ \frac {4}{5} x^{5} + \frac {4}{3} x^{3} + 2 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="fricas")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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giac [A]  time = 0.36, size = 17, normalized size = 0.81 \[ \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="giac")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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maple [A]  time = 0.00, size = 18, normalized size = 0.86 \[ \frac {4}{5} x^{5}+\frac {4}{3} x^{3}+2 x^{2}+x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^4+4*x^2+4*x+1,x)

[Out]

x+2*x^2+4/3*x^3+4/5*x^5

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maxima [A]  time = 0.57, size = 17, normalized size = 0.81 \[ \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="maxima")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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mupad [B]  time = 0.03, size = 17, normalized size = 0.81 \[ \frac {4\,x^5}{5}+\frac {4\,x^3}{3}+2\,x^2+x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x + 4*x^2 + 4*x^4 + 1,x)

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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sympy [A]  time = 0.06, size = 19, normalized size = 0.90 \[ \frac {4 x^{5}}{5} + \frac {4 x^{3}}{3} + 2 x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x**4+4*x**2+4*x+1,x)

[Out]

4*x**5/5 + 4*x**3/3 + 2*x**2 + x

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