\(\int (15+\sqrt [25]{e}+2 x) \, dx\) [9424]

Optimal result

Integrand size = 10, antiderivative size = 12 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=(2+x) \left (13+\sqrt [25]{e}+x\right ) \]

[Out]

(2+x)*(13+x+exp(1/25))

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^2+\left (15+\sqrt [25]{e}\right ) x \]

[In]

Int[15 + E^(1/25) + 2*x,x]

[Out]

(15 + E^(1/25))*x + x^2

Rubi steps \begin{align*} \text {integral}& = \left (15+\sqrt [25]{e}\right ) x+x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=15 x+\sqrt [25]{e} x+x^2 \]

[In]

Integrate[15 + E^(1/25) + 2*x,x]

[Out]

15*x + E^(1/25)*x + x^2

Maple [A] (verified)

Time = 0.11 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
norman	\(x^{2}+\left ({\mathrm e}^{\frac {1}{25}}+15\right ) x\)	\(11\)
parallelrisch	\(x^{2}+\left ({\mathrm e}^{\frac {1}{25}}+15\right ) x\)	\(11\)
gosper	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)
default	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)
risch	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)
parts	\(x \,{\mathrm e}^{\frac {1}{25}}+x^{2}+15 x\)	\(12\)

[In]

int(exp(1/25)+2*x+15,x,method=_RETURNVERBOSE)

[Out]

x^2+(exp(1/25)+15)*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^{2} + x e^{\frac {1}{25}} + 15 \, x \]

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="fricas")

[Out]

x^2 + x*e^(1/25) + 15*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^{2} + x \left (e^{\frac {1}{25}} + 15\right ) \]

[In]

integrate(exp(1/25)+2*x+15,x)

[Out]

x**2 + x*(exp(1/25) + 15)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^{2} + x e^{\frac {1}{25}} + 15 \, x \]

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="maxima")

[Out]

x^2 + x*e^(1/25) + 15*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^{2} + x e^{\frac {1}{25}} + 15 \, x \]

[In]

integrate(exp(1/25)+2*x+15,x, algorithm="giac")

[Out]

x^2 + x*e^(1/25) + 15*x

Mupad [B] (verification not implemented)

Time = 13.94 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (15+\sqrt [25]{e}+2 x\right ) \, dx=x^2+\left ({\mathrm {e}}^{1/25}+15\right )\,x \]

[In]

int(2*x + exp(1/25) + 15,x)

[Out]

x*(exp(1/25) + 15) + x^2