Optimal. Leaf size=44 \[ \frac {3 \left (a+b x+c x^2\right )^{7/3}}{7 d \left (b^2-4 a c\right ) (b d+2 c d x)^{14/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {682} \[ \frac {3 \left (a+b x+c x^2\right )^{7/3}}{7 d \left (b^2-4 a c\right ) (b d+2 c d x)^{14/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 682
Rubi steps
\begin {align*} \int \frac {\left (a+b x+c x^2\right )^{4/3}}{(b d+2 c d x)^{17/3}} \, dx &=\frac {3 \left (a+b x+c x^2\right )^{7/3}}{7 \left (b^2-4 a c\right ) d (b d+2 c d x)^{14/3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 50, normalized size = 1.14 \[ \frac {3 (a+x (b+c x))^{7/3} \sqrt [3]{d (b+2 c x)}}{7 d^6 \left (b^2-4 a c\right ) (b+2 c x)^5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.36, size = 194, normalized size = 4.41 \[ \frac {3 \, {\left (c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left (b^{2} + 2 \, a c\right )} x^{2} + a^{2}\right )} {\left (2 \, c d x + b d\right )}^{\frac {1}{3}} {\left (c x^{2} + b x + a\right )}^{\frac {1}{3}}}{7 \, {\left (32 \, {\left (b^{2} c^{5} - 4 \, a c^{6}\right )} d^{6} x^{5} + 80 \, {\left (b^{3} c^{4} - 4 \, a b c^{5}\right )} d^{6} x^{4} + 80 \, {\left (b^{4} c^{3} - 4 \, a b^{2} c^{4}\right )} d^{6} x^{3} + 40 \, {\left (b^{5} c^{2} - 4 \, a b^{3} c^{3}\right )} d^{6} x^{2} + 10 \, {\left (b^{6} c - 4 \, a b^{4} c^{2}\right )} d^{6} x + {\left (b^{7} - 4 \, a b^{5} c\right )} d^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (c x^{2} + b x + a\right )}^{\frac {4}{3}}}{{\left (2 \, c d x + b d\right )}^{\frac {17}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 44, normalized size = 1.00 \[ -\frac {3 \left (2 c x +b \right ) \left (c \,x^{2}+b x +a \right )^{\frac {7}{3}}}{7 \left (4 a c -b^{2}\right ) \left (2 c d x +b d \right )^{\frac {17}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (c x^{2} + b x + a\right )}^{\frac {4}{3}}}{{\left (2 \, c d x + b d\right )}^{\frac {17}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {{\left (c\,x^2+b\,x+a\right )}^{4/3}}{{\left (b\,d+2\,c\,d\,x\right )}^{17/3}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________