3.240 \(\int 2^{\log (-8+7 x)} \, dx\)

Optimal. Leaf size=20 \[ \frac{(7 x-8)^{1+\log (2)}}{7 (1+\log (2))} \]

[Out]

(-8 + 7*x)^(1 + Log[2])/(7*(1 + Log[2]))

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Rubi [A]  time = 0.004664, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2274, 32} \[ \frac{(7 x-8)^{1+\log (2)}}{7 (1+\log (2))} \]

Antiderivative was successfully verified.

[In]

Int[2^Log[-8 + 7*x],x]

[Out]

(-8 + 7*x)^(1 + Log[2])/(7*(1 + Log[2]))

Rule 2274

Int[(u_.)*(F_)^((a_.)*(Log[z_]*(b_.) + (v_.))), x_Symbol] :> Int[u*F^(a*v)*z^(a*b*Log[F]), x] /; FreeQ[{F, a,
b}, x]

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

\begin{align*} \int 2^{\log (-8+7 x)} \, dx &=\int (-8+7 x)^{\log (2)} \, dx\\ &=\frac{(-8+7 x)^{1+\log (2)}}{7 (1+\log (2))}\\ \end{align*}

Mathematica [A]  time = 0.0067256, size = 20, normalized size = 1. \[ \frac{(7 x-8) 2^{\log (7 x-8)}}{7+\log (128)} \]

Antiderivative was successfully verified.

[In]

Integrate[2^Log[-8 + 7*x],x]

[Out]

(2^Log[-8 + 7*x]*(-8 + 7*x))/(7 + Log[128])

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Maple [A]  time = 0.007, size = 22, normalized size = 1.1 \begin{align*}{\frac{ \left ( -8+7\,x \right ){2}^{\ln \left ( -8+7\,x \right ) }}{7\,\ln \left ( 2 \right ) +7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^ln(-8+7*x),x)

[Out]

1/7*(-8+7*x)/(1+ln(2))*2^ln(-8+7*x)

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Maxima [A]  time = 0.991234, size = 39, normalized size = 1.95 \begin{align*} \frac{2^{{\left (\frac{1}{\log \left (2\right )} + 1\right )} \log \left (7 \, x - 8\right )}}{7 \,{\left (\frac{1}{\log \left (2\right )} + 1\right )} \log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^log(-8+7*x),x, algorithm="maxima")

[Out]

1/7*2^((1/log(2) + 1)*log(7*x - 8))/((1/log(2) + 1)*log(2))

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Fricas [A]  time = 1.8078, size = 70, normalized size = 3.5 \begin{align*} \frac{{\left (7 \, x - 8\right )} e^{\left (\log \left (2\right ) \log \left (7 \, x - 8\right )\right )}}{7 \,{\left (\log \left (2\right ) + 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^log(-8+7*x),x, algorithm="fricas")

[Out]

1/7*(7*x - 8)*e^(log(2)*log(7*x - 8))/(log(2) + 1)

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Sympy [B]  time = 0.505494, size = 34, normalized size = 1.7 \begin{align*} \frac{7 \cdot 2^{\log{\left (7 x - 8 \right )}} x}{7 \log{\left (2 \right )} + 7} - \frac{8 \cdot 2^{\log{\left (7 x - 8 \right )}}}{7 \log{\left (2 \right )} + 7} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2**ln(-8+7*x),x)

[Out]

7*2**log(7*x - 8)*x/(7*log(2) + 7) - 8*2**log(7*x - 8)/(7*log(2) + 7)

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Giac [A]  time = 1.21184, size = 31, normalized size = 1.55 \begin{align*} \frac{{\left (7 \, x - 8\right )} e^{\left (\log \left (2\right ) \log \left (7 \, x - 8\right )\right )}}{7 \,{\left (\log \left (2\right ) + 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^log(-8+7*x),x, algorithm="giac")

[Out]

1/7*(7*x - 8)*e^(log(2)*log(7*x - 8))/(log(2) + 1)