3.100.95 \(\int (3 e^x-8 x^7) \, dx\)

Optimal. Leaf size=12 \[ 4+3 e^x-x^8 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} 3 e^x-x^8 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*E^x - 8*x^7,x]

[Out]

3*E^x - x^8

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 {gather*} \begin {aligned} \text {integral} &=-x^8+3 \int e^x \, dx\\ &=3 e^x-x^8\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} 3 e^x-x^8 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*E^x - 8*x^7,x]

[Out]

3*E^x - x^8

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fricas [A]  time = 2.08, size = 10, normalized size = 0.83 \begin {gather*} -x^{8} + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)-8*x^7,x, algorithm="fricas")

[Out]

-x^8 + 3*e^x

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giac [A]  time = 0.23, size = 10, normalized size = 0.83 \begin {gather*} -x^{8} + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)-8*x^7,x, algorithm="giac")

[Out]

-x^8 + 3*e^x

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maple [A]  time = 0.01, size = 11, normalized size = 0.92

method	result	size
default	\(-x^{8}+3 \,{\mathrm e}^{x}\)	\(11\)
norman	\(-x^{8}+3 \,{\mathrm e}^{x}\)	\(11\)
risch	\(-x^{8}+3 \,{\mathrm e}^{x}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x)-8*x^7,x,method=_RETURNVERBOSE)

[Out]

-x^8+3*exp(x)

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maxima [A]  time = 0.36, size = 10, normalized size = 0.83 \begin {gather*} -x^{8} + 3 \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)-8*x^7,x, algorithm="maxima")

[Out]

-x^8 + 3*e^x

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mupad [B]  time = 7.45, size = 10, normalized size = 0.83 \begin {gather*} 3\,{\mathrm {e}}^x-x^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x) - 8*x^7,x)

[Out]

3*exp(x) - x^8

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sympy [A]  time = 0.07, size = 7, normalized size = 0.58 \begin {gather*} - x^{8} + 3 e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(x)-8*x**7,x)

[Out]

-x**8 + 3*exp(x)

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