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]

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

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Rubi [A]  time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, 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 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]

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]

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*}

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Mathematica [A]  time = 0.01, size = 20, normalized size = 1.00 \[ \frac {(7 x-8) 2^{\log (7 x-8)}}{7+\log (128)} \]

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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fricas [A]  time = 0.44, size = 23, normalized size = 1.15 \[ \frac {{\left (7 \, x - 8\right )} e^{\left (\log \relax (2) \log \left (7 \, x - 8\right )\right )}}{7 \, {\left (\log \relax (2) + 1\right )}} \]

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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giac [A]  time = 0.18, size = 23, normalized size = 1.15 \[ \frac {{\left (7 \, x - 8\right )} e^{\left (\log \relax (2) \log \left (7 \, x - 8\right )\right )}}{7 \, {\left (\log \relax (2) + 1\right )}} \]

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)

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maple [A]  time = 0.07, size = 22, normalized size = 1.10 \[ \frac {\left (7 x -8\right ) 2^{\ln \left (7 x -8\right )}}{7 \ln \relax (2)+7} \]

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 = 0.59, size = 29, normalized size = 1.45 \[ \frac {2^{{\left (\frac {1}{\log \relax (2)} + 1\right )} \log \left (7 \, x - 8\right )}}{7 \, {\left (\frac {1}{\log \relax (2)} + 1\right )} \log \relax (2)} \]

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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mupad [B]  time = 0.39, size = 19, normalized size = 0.95 \[ \frac {{\left (7\,x-8\right )}^{\ln \relax (2)+1}}{7\,\left (\ln \relax (2)+1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^log(7*x - 8),x)

[Out]

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

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sympy [B]  time = 0.49, size = 34, normalized size = 1.70 \[ \frac {7 \cdot 2^{\log {\left (7 x - 8 \right )}} x}{7 \log {\relax (2 )} + 7} - \frac {8 \cdot 2^{\log {\left (7 x - 8 \right )}}}{7 \log {\relax (2 )} + 7} \]

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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