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

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

[Out]

F^(2 + 5*x)/(5*Log[F])

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Rubi [A]  time = 0.002795, antiderivative size = 15, normalized size of antiderivative = 1., 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*}

Mathematica [A]  time = 0.0036337, size = 15, normalized size = 1. \[ \frac{F^{5 x+2}}{5 \log (F)} \]

Antiderivative was successfully verified.

[In]

Integrate[F^(2 + 5*x),x]

[Out]

F^(2 + 5*x)/(5*Log[F])

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Maple [A]  time = 0.004, size = 14, normalized size = 0.9 \begin{align*}{\frac{{F}^{2+5\,x}}{5\,\ln \left ( F \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 1.12231, size = 18, normalized size = 1.2 \begin{align*} \frac{F^{5 \, x + 2}}{5 \, \log \left (F\right )} \end{align*}

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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Fricas [A]  time = 1.50043, size = 32, normalized size = 2.13 \begin{align*} \frac{F^{5 \, x + 2}}{5 \, \log \left (F\right )} \end{align*}

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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Sympy [A]  time = 0.094902, size = 15, normalized size = 1. \begin{align*} \begin{cases} \frac{F^{5 x + 2}}{5 \log{\left (F \right )}} & \text{for}\: 5 \log{\left (F \right )} \neq 0 \\x & \text{otherwise} \end{cases} \end{align*}

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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Giac [A]  time = 1.21063, size = 18, normalized size = 1.2 \begin{align*} \frac{F^{5 \, x + 2}}{5 \, \log \left (F\right )} \end{align*}

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)