3.36 \(\int (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4) \, dx\)

Optimal. Leaf size=32 \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]

[Out]

4*a*c*x+4/3*c^2*x^3+c*d*x^4+1/5*d^2*x^5

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]

Antiderivative was successfully verified.

[In]

Int[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4,x]

[Out]

4*a*c*x + (4*c^2*x^3)/3 + c*d*x^4 + (d^2*x^5)/5

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 32, normalized size = 1.00 \[ 4 a c x+\frac {4 c^2 x^3}{3}+c d x^4+\frac {d^2 x^5}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4,x]

[Out]

4*a*c*x + (4*c^2*x^3)/3 + c*d*x^4 + (d^2*x^5)/5

________________________________________________________________________________________

fricas [A]  time = 0.39, size = 28, normalized size = 0.88 \[ \frac {1}{5} x^{5} d^{2} + x^{4} d c + \frac {4}{3} x^{3} c^{2} + 4 x c a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c,x, algorithm="fricas")

[Out]

1/5*x^5*d^2 + x^4*d*c + 4/3*x^3*c^2 + 4*x*c*a

________________________________________________________________________________________

giac [A]  time = 0.27, size = 28, normalized size = 0.88 \[ \frac {1}{5} \, d^{2} x^{5} + c d x^{4} + \frac {4}{3} \, c^{2} x^{3} + 4 \, a c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c,x, algorithm="giac")

[Out]

1/5*d^2*x^5 + c*d*x^4 + 4/3*c^2*x^3 + 4*a*c*x

________________________________________________________________________________________

maple [A]  time = 0.00, size = 29, normalized size = 0.91 \[ \frac {1}{5} d^{2} x^{5}+c d \,x^{4}+\frac {4}{3} c^{2} x^{3}+4 a c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c,x)

[Out]

4*a*c*x+4/3*c^2*x^3+c*d*x^4+1/5*d^2*x^5

________________________________________________________________________________________

maxima [A]  time = 0.65, size = 28, normalized size = 0.88 \[ \frac {1}{5} \, d^{2} x^{5} + c d x^{4} + \frac {4}{3} \, c^{2} x^{3} + 4 \, a c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c,x, algorithm="maxima")

[Out]

1/5*d^2*x^5 + c*d*x^4 + 4/3*c^2*x^3 + 4*a*c*x

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 28, normalized size = 0.88 \[ \frac {4\,c^2\,x^3}{3}+c\,d\,x^4+4\,a\,c\,x+\frac {d^2\,x^5}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3,x)

[Out]

(4*c^2*x^3)/3 + (d^2*x^5)/5 + 4*a*c*x + c*d*x^4

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 31, normalized size = 0.97 \[ 4 a c x + \frac {4 c^{2} x^{3}}{3} + c d x^{4} + \frac {d^{2} x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(d**2*x**4+4*c*d*x**3+4*c**2*x**2+4*a*c,x)

[Out]

4*a*c*x + 4*c**2*x**3/3 + c*d*x**4 + d**2*x**5/5

________________________________________________________________________________________