Optimal. Leaf size=98 \[ \frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}-\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}-\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.207649, antiderivative size = 98, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{3 a^{2 x (k+l)}}{\log (a) (k+l)}-\frac{4 a^{x (3 k+l)}}{\log (a) (3 k+l)}-\frac{4 a^{x (k+3 l)}}{\log (a) (k+3 l)}+\frac{a^{4 k x}}{4 k \log (a)}+\frac{a^{4 l x}}{4 l \log (a)} \]
Antiderivative was successfully verified.
[In] Int[(a^(k*x) - a^(l*x))^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (a^{k x} - a^{l x}\right )^{4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a**(k*x)-a**(l*x))**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.110412, size = 80, normalized size = 0.82 \[ \frac{\frac{12 a^{2 x (k+l)}}{k+l}-\frac{16 a^{x (3 k+l)}}{3 k+l}-\frac{16 a^{x (k+3 l)}}{k+3 l}+\frac{a^{4 k x}}{k}+\frac{a^{4 l x}}{l}}{4 \log (a)} \]
Antiderivative was successfully verified.
[In] Integrate[(a^(k*x) - a^(l*x))^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.026, size = 109, normalized size = 1.1 \[{\frac{ \left ({a}^{kx} \right ) ^{4}}{4\,k\ln \left ( a \right ) }}-4\,{\frac{ \left ({a}^{kx} \right ) ^{3}{a}^{lx}}{\ln \left ( a \right ) \left ( 3\,k+l \right ) }}+3\,{\frac{ \left ({a}^{kx} \right ) ^{2} \left ({a}^{lx} \right ) ^{2}}{\ln \left ( a \right ) \left ( k+l \right ) }}-4\,{\frac{{a}^{kx} \left ({a}^{lx} \right ) ^{3}}{\ln \left ( a \right ) \left ( k+3\,l \right ) }}+{\frac{ \left ({a}^{lx} \right ) ^{4}}{4\,l\ln \left ( a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a^(k*x)-a^(l*x))^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34728, size = 134, normalized size = 1.37 \[ -\frac{4 \, a^{3 \, k x + l x}}{{\left (3 \, k + l\right )} \log \left (a\right )} - \frac{4 \, a^{k x + 3 \, l x}}{{\left (k + 3 \, l\right )} \log \left (a\right )} + \frac{3 \, a^{2 \, k x + 2 \, l x}}{{\left (k + l\right )} \log \left (a\right )} + \frac{a^{4 \, k x}}{4 \, k \log \left (a\right )} + \frac{a^{4 \, l x}}{4 \, l \log \left (a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a^(k*x) - a^(l*x))^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215607, size = 279, normalized size = 2.85 \[ -\frac{16 \,{\left (3 \, k^{3} l + 4 \, k^{2} l^{2} + k l^{3}\right )} a^{k x} a^{3 \, l x} - 12 \,{\left (3 \, k^{3} l + 10 \, k^{2} l^{2} + 3 \, k l^{3}\right )} a^{2 \, k x} a^{2 \, l x} + 16 \,{\left (k^{3} l + 4 \, k^{2} l^{2} + 3 \, k l^{3}\right )} a^{3 \, k x} a^{l x} -{\left (3 \, k^{3} l + 13 \, k^{2} l^{2} + 13 \, k l^{3} + 3 \, l^{4}\right )} a^{4 \, k x} -{\left (3 \, k^{4} + 13 \, k^{3} l + 13 \, k^{2} l^{2} + 3 \, k l^{3}\right )} a^{4 \, l x}}{4 \,{\left (3 \, k^{4} l + 13 \, k^{3} l^{2} + 13 \, k^{2} l^{3} + 3 \, k l^{4}\right )} \log \left (a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a^(k*x) - a^(l*x))^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a**(k*x)-a**(l*x))**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.266916, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a^(k*x) - a^(l*x))^4,x, algorithm="giac")
[Out]