\(\int \frac {4 x^3}{\log ^2(2)} \, dx\) [6078]

Optimal result

Integrand size = 9, antiderivative size = 8 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^4}{\log ^2(2)} \]

[Out]

x^4/ln(2)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 30} \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^4}{\log ^2(2)} \]

[In]

Int[(4*x^3)/Log[2]^2,x]

[Out]

x^4/Log[2]^2

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{align*} \text {integral}& = \frac {4 \int x^3 \, dx}{\log ^2(2)} \\ & = \frac {x^4}{\log ^2(2)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^4}{\log ^2(2)} \]

[In]

Integrate[(4*x^3)/Log[2]^2,x]

[Out]

x^4/Log[2]^2

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12

method	result	size
gosper	\(\frac {x^{4}}{\ln \left (2\right )^{2}}\)	\(9\)
default	\(\frac {x^{4}}{\ln \left (2\right )^{2}}\)	\(9\)
norman	\(\frac {x^{4}}{\ln \left (2\right )^{2}}\)	\(9\)
risch	\(\frac {x^{4}}{\ln \left (2\right )^{2}}\)	\(9\)
parallelrisch	\(\frac {x^{4}}{\ln \left (2\right )^{2}}\)	\(9\)

[In]

int(4*x^3/ln(2)^2,x,method=_RETURNVERBOSE)

[Out]

x^4/ln(2)^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^{4}}{\log \left (2\right )^{2}} \]

[In]

integrate(4*x^3/log(2)^2,x, algorithm="fricas")

[Out]

x^4/log(2)^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^{4}}{\log {\left (2 \right )}^{2}} \]

[In]

integrate(4*x**3/ln(2)**2,x)

[Out]

x**4/log(2)**2

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^{4}}{\log \left (2\right )^{2}} \]

[In]

integrate(4*x^3/log(2)^2,x, algorithm="maxima")

[Out]

x^4/log(2)^2

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^{4}}{\log \left (2\right )^{2}} \]

[In]

integrate(4*x^3/log(2)^2,x, algorithm="giac")

[Out]

x^4/log(2)^2

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {4 x^3}{\log ^2(2)} \, dx=\frac {x^4}{{\ln \left (2\right )}^2} \]

[In]

int((4*x^3)/log(2)^2,x)

[Out]

x^4/log(2)^2