Optimal. Leaf size=18 \[ \frac{(d+e x)^{m+1}}{e (m+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0142773, antiderivative size = 18, 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 \[ \frac{(d+e x)^{m+1}}{e (m+1)} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^m,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.78324, size = 12, normalized size = 0.67 \[ \frac{\left (d + e x\right )^{m + 1}}{e \left (m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**m,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0113396, size = 17, normalized size = 0.94 \[ \frac{(d+e x)^{m+1}}{e m+e} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^m,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 19, normalized size = 1.1 \[{\frac{ \left ( ex+d \right ) ^{1+m}}{e \left ( 1+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^m,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.233574, size = 27, normalized size = 1.5 \[ \frac{{\left (e x + d\right )}{\left (e x + d\right )}^{m}}{e m + e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.077394, size = 20, normalized size = 1.11 \[ \frac{\begin{cases} \frac{\left (d + e x\right )^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left (d + e x \right )} & \text{otherwise} \end{cases}}{e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)**m,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.204059, size = 24, normalized size = 1.33 \[ \frac{{\left (x e + d\right )}^{m + 1} e^{\left (-1\right )}}{m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)^m,x, algorithm="giac")
[Out]