3.4.84 \(\int 3 x^2 \, dx\)

Optimal. Leaf size=7 \[ e^5+x^3 \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 3, normalized size of antiderivative = 0.43, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \begin {gather*} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*x^2,x]

[Out]

x^3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=3 \int x^2 \, dx\\ &=x^3\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 3, normalized size = 0.43 \begin {gather*} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*x^2,x]

[Out]

x^3

________________________________________________________________________________________

fricas [A]  time = 0.67, size = 3, normalized size = 0.43 \begin {gather*} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2,x, algorithm="fricas")

[Out]

x^3

________________________________________________________________________________________

giac [A]  time = 0.31, size = 3, normalized size = 0.43 \begin {gather*} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2,x, algorithm="giac")

[Out]

x^3

________________________________________________________________________________________

maple [A]  time = 0.01, size = 4, normalized size = 0.57

method	result	size
gosper	\(x^{3}\)	\(4\)
default	\(x^{3}\)	\(4\)
norman	\(x^{3}\)	\(4\)
risch	\(x^{3}\)	\(4\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2,x,method=_RETURNVERBOSE)

[Out]

x^3

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 3, normalized size = 0.43 \begin {gather*} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2,x, algorithm="maxima")

[Out]

x^3

________________________________________________________________________________________

mupad [B]  time = 0.01, size = 3, normalized size = 0.43 \begin {gather*} x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2,x)

[Out]

x^3

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 2, normalized size = 0.29 \begin {gather*} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2,x)

[Out]

x**3

________________________________________________________________________________________