Optimal. Leaf size=201 \[ \frac {\sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} \sqrt [3]{d} \sqrt [3]{a b+(-a-b) x+x^2}}{-2 a+2 x+\sqrt [3]{d} \sqrt [3]{a b+(-a-b) x+x^2}}\right )}{d^{2/3}}+\frac {\log \left (a-x+\sqrt [3]{d} \sqrt [3]{a b+(-a-b) x+x^2}\right )}{d^{2/3}}-\frac {\log \left (a^2-2 a x+x^2+\left (-a \sqrt [3]{d}+\sqrt [3]{d} x\right ) \sqrt [3]{a b+(-a-b) x+x^2}+d^{2/3} \left (a b+(-a-b) x+x^2\right )^{2/3}\right )}{2 d^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} \left (a^2+b d-(2 a+d) x+x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} \left (a^2+b d-(2 a+d) x+x^2\right )} \, dx &=\int \frac {a-2 b+x}{\sqrt [3]{a b+(-a-b) x+x^2} \left (a^2+b d+(-2 a-d) x+x^2\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 4.83, size = 181, normalized size = 0.90 \begin {gather*} \frac {\sqrt [3]{-a+x} \sqrt [3]{-b+x} \left (2 \sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} \sqrt [3]{d} \sqrt [3]{-b+x}}{2 (-a+x)^{2/3}+\sqrt [3]{d} \sqrt [3]{-b+x}}\right )+2 \log \left ((-a+x)^{2/3}-\sqrt [3]{d} \sqrt [3]{-b+x}\right )-\log \left ((-a+x)^{4/3}+\sqrt [3]{d} (-a+x)^{2/3} \sqrt [3]{-b+x}+d^{2/3} (-b+x)^{2/3}\right )\right )}{2 d^{2/3} \sqrt [3]{(-a+x) (-b+x)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.17, size = 0, normalized size = 0.00 \[\int \frac {a -2 b +x}{\left (\left (-a +x \right ) \left (-b +x \right )\right )^{\frac {1}{3}} \left (a^{2}+b d -\left (2 a +d \right ) x +x^{2}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {a-2\,b+x}{{\left (\left (a-x\right )\,\left (b-x\right )\right )}^{1/3}\,\left (b\,d-x\,\left (2\,a+d\right )+a^2+x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________