3.194 \(\int e^{-0.1 x} x \, dx\)

Optimal. Leaf size=16 \[ -10. e^{-0.1 x} x-100. e^{-0.1 x} \]

[Out]

-100./E^(0.1*x) - (10.*x)/E^(0.1*x)

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Rubi [A]  time = 0.0146795, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ -10. e^{-0.1 x} x-100. e^{-0.1 x} \]

Warning: Unable to verify antiderivative.

[In]  Int[x/E^(0.1*x),x]

[Out]

-100./E^(0.1*x) - (10.*x)/E^(0.1*x)

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Rubi in Sympy [A]  time = 2.32485, size = 15, normalized size = 0.94 \[ - 10.0 x e^{- 0.1 x} - 100.0 e^{- 0.1 x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(-.1*x)*x,x)

[Out]

-10.0*x*exp(-0.1*x) - 100.0*exp(-0.1*x)

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Mathematica [A]  time = 0.00239891, size = 11, normalized size = 0.69 \[ e^{-0.1 x} (-10. x-100.) \]

Warning: Unable to verify antiderivative.

[In]  Integrate[x/E^(0.1*x),x]

[Out]

(-99.99999999999999 - 10.*x)/E^(0.1*x)

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Maple [A]  time = 0.016, size = 10, normalized size = 0.6 \[ - 10.0\, \left ( x+ 10.0 \right ){{\rm e}^{- 0.1000000000\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(-.1*x)*x,x)

[Out]

-10.*(x+10.)*exp(-.1000000000*x)

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Maxima [A]  time = 0.93581, size = 12, normalized size = 0.75 \[ -10 \,{\left (x + 10\right )} e^{\left (-\frac{1}{10} \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(-0.100000000000000*x),x, algorithm="maxima")

[Out]

-10*(x + 10)*e^(-1/10*x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(-0.100000000000000*x),x, algorithm="fricas")

[Out]

Exception raised: TypeError

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Sympy [A]  time = 0.141498, size = 10, normalized size = 0.62 \[ 1.0 \left (- 10.0 x - 100.0\right ) e^{- 0.1 x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(-.1*x)*x,x)

[Out]

1.0*(-10.0*x - 100.0)*exp(-0.1*x)

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GIAC/XCAS [A]  time = 0.235451, size = 14, normalized size = 0.88 \[{\left (-10.0 \, x - 100.0\right )} e^{\left (-0.1 \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*e^(-0.100000000000000*x),x, algorithm="giac")

[Out]

(-10.0*x - 100.0)*e^(-0.1*x)