3.27 \(\int F^{2+5 x} \, dx\)

Optimal. Leaf size=15 \[ \frac {F^{5 x+2}}{5 \log (F)} \]

[Out]

1/5*F^(2+5*x)/ln(F)

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2194} \[ \frac {F^{5 x+2}}{5 \log (F)} \]

Antiderivative was successfully verified.

[In]

Int[F^(2 + 5*x),x]

[Out]

F^(2 + 5*x)/(5*Log[F])

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {align*} \int F^{2+5 x} \, dx &=\frac {F^{2+5 x}}{5 \log (F)}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \[ \frac {F^{5 x+2}}{5 \log (F)} \]

Antiderivative was successfully verified.

[In]

Integrate[F^(2 + 5*x),x]

[Out]

F^(2 + 5*x)/(5*Log[F])

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fricas [A]  time = 0.41, size = 13, normalized size = 0.87 \[ \frac {F^{5 \, x + 2}}{5 \, \log \relax (F)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(2+5*x),x, algorithm="fricas")

[Out]

1/5*F^(5*x + 2)/log(F)

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giac [A]  time = 0.26, size = 13, normalized size = 0.87 \[ \frac {F^{5 \, x + 2}}{5 \, \log \relax (F)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(2+5*x),x, algorithm="giac")

[Out]

1/5*F^(5*x + 2)/log(F)

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maple [A]  time = 0.01, size = 14, normalized size = 0.93 \[ \frac {F^{5 x +2}}{5 \ln \relax (F )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(5*x+2),x)

[Out]

1/5*F^(5*x+2)/ln(F)

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maxima [A]  time = 0.43, size = 13, normalized size = 0.87 \[ \frac {F^{5 \, x + 2}}{5 \, \log \relax (F)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(2+5*x),x, algorithm="maxima")

[Out]

1/5*F^(5*x + 2)/log(F)

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mupad [B]  time = 3.54, size = 13, normalized size = 0.87 \[ \frac {F^{5\,x+2}}{5\,\ln \relax (F)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F^(5*x + 2),x)

[Out]

F^(5*x + 2)/(5*log(F))

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sympy [A]  time = 0.09, size = 15, normalized size = 1.00 \[ \begin {cases} \frac {F^{5 x + 2}}{5 \log {\relax (F )}} & \text {for}\: 5 \log {\relax (F )} \neq 0 \\x & \text {otherwise} \end {cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F**(2+5*x),x)

[Out]

Piecewise((F**(5*x + 2)/(5*log(F)), Ne(5*log(F), 0)), (x, True))

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