Optimal. Leaf size=68 \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} a e x^3+\frac {1}{4} a f x^4+\frac {1}{5} b c x^5+\frac {1}{6} b d x^6+\frac {1}{7} b e x^7+\frac {1}{8} b f x^8 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 68, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1850} \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} a e x^3+\frac {1}{4} a f x^4+\frac {1}{5} b c x^5+\frac {1}{6} b d x^6+\frac {1}{7} b e x^7+\frac {1}{8} b f x^8 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1850
Rubi steps
\begin {align*} \int \left (c+d x+e x^2+f x^3\right ) \left (a+b x^4\right ) \, dx &=\int \left (a c+a d x+a e x^2+a f x^3+b c x^4+b d x^5+b e x^6+b f x^7\right ) \, dx\\ &=a c x+\frac {1}{2} a d x^2+\frac {1}{3} a e x^3+\frac {1}{4} a f x^4+\frac {1}{5} b c x^5+\frac {1}{6} b d x^6+\frac {1}{7} b e x^7+\frac {1}{8} b f x^8\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 68, normalized size = 1.00 \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} a e x^3+\frac {1}{4} a f x^4+\frac {1}{5} b c x^5+\frac {1}{6} b d x^6+\frac {1}{7} b e x^7+\frac {1}{8} b f x^8 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.37, size = 54, normalized size = 0.79 \[ \frac {1}{8} x^{8} f b + \frac {1}{7} x^{7} e b + \frac {1}{6} x^{6} d b + \frac {1}{5} x^{5} c b + \frac {1}{4} x^{4} f a + \frac {1}{3} x^{3} e a + \frac {1}{2} x^{2} d a + x c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 56, normalized size = 0.82 \[ \frac {1}{8} \, b f x^{8} + \frac {1}{7} \, b x^{7} e + \frac {1}{6} \, b d x^{6} + \frac {1}{5} \, b c x^{5} + \frac {1}{4} \, a f x^{4} + \frac {1}{3} \, a x^{3} e + \frac {1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 55, normalized size = 0.81 \[ \frac {1}{8} b f \,x^{8}+\frac {1}{7} b e \,x^{7}+\frac {1}{6} b d \,x^{6}+\frac {1}{5} b c \,x^{5}+\frac {1}{4} a f \,x^{4}+\frac {1}{3} a e \,x^{3}+\frac {1}{2} a d \,x^{2}+a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 54, normalized size = 0.79 \[ \frac {1}{8} \, b f x^{8} + \frac {1}{7} \, b e x^{7} + \frac {1}{6} \, b d x^{6} + \frac {1}{5} \, b c x^{5} + \frac {1}{4} \, a f x^{4} + \frac {1}{3} \, a e x^{3} + \frac {1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 54, normalized size = 0.79 \[ \frac {b\,f\,x^8}{8}+\frac {b\,e\,x^7}{7}+\frac {b\,d\,x^6}{6}+\frac {b\,c\,x^5}{5}+\frac {a\,f\,x^4}{4}+\frac {a\,e\,x^3}{3}+\frac {a\,d\,x^2}{2}+a\,c\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 63, normalized size = 0.93 \[ a c x + \frac {a d x^{2}}{2} + \frac {a e x^{3}}{3} + \frac {a f x^{4}}{4} + \frac {b c x^{5}}{5} + \frac {b d x^{6}}{6} + \frac {b e x^{7}}{7} + \frac {b f x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________