3.93.47 \(\int \frac {20 x}{\log (4)} \, dx\) [9247]

Optimal. Leaf size=9 \[ \frac {10 x^2}{\log (4)} \]

[Out]

5*x^2/ln(2)

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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30} \begin {gather*} \frac {10 x^2}{\log (4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(20*x)/Log[4],x]

[Out]

(10*x^2)/Log[4]

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} &=\frac {20 \int x \, dx}{\log (4)}\\ &=\frac {10 x^2}{\log (4)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {10 x^2}{\log (4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(20*x)/Log[4],x]

[Out]

(10*x^2)/Log[4]

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Maple [A]
time = 0.34, size = 10, normalized size = 1.11

method	result	size
gosper	\(\frac {5 x^{2}}{\ln \left (2\right )}\)	\(10\)
default	\(\frac {5 x^{2}}{\ln \left (2\right )}\)	\(10\)
norman	\(\frac {5 x^{2}}{\ln \left (2\right )}\)	\(10\)
risch	\(\frac {5 x^{2}}{\ln \left (2\right )}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x/ln(2),x,method=_RETURNVERBOSE)

[Out]

5*x^2/ln(2)

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Maxima [A]
time = 0.26, size = 9, normalized size = 1.00 \begin {gather*} \frac {5 \, x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/log(2),x, algorithm="maxima")

[Out]

5*x^2/log(2)

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Fricas [A]
time = 0.34, size = 9, normalized size = 1.00 \begin {gather*} \frac {5 \, x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/log(2),x, algorithm="fricas")

[Out]

5*x^2/log(2)

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Sympy [A]
time = 0.01, size = 7, normalized size = 0.78 \begin {gather*} \frac {5 x^{2}}{\log {\left (2 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/ln(2),x)

[Out]

5*x**2/log(2)

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Giac [A]
time = 0.41, size = 9, normalized size = 1.00 \begin {gather*} \frac {5 \, x^{2}}{\log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x/log(2),x, algorithm="giac")

[Out]

5*x^2/log(2)

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Mupad [B]
time = 0.03, size = 9, normalized size = 1.00 \begin {gather*} \frac {5\,x^2}{\ln \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x)/log(2),x)

[Out]

(5*x^2)/log(2)

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