Integrand size = 31, antiderivative size = 1637 \[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\frac {a d^2 \left (c^2 f^2-g^2\right )^2 \sqrt {d-c^2 d x^2}}{g^5}-\frac {2 b c d^2 x \sqrt {d-c^2 d x^2}}{15 g \sqrt {1-c^2 x^2}}-\frac {b c d^2 \left (c^2 f^2-2 g^2\right ) x \sqrt {d-c^2 d x^2}}{3 g^3 \sqrt {1-c^2 x^2}}+\frac {b c d^2 \left (c^2 f^2-g^2\right )^2 x \sqrt {d-c^2 d x^2}}{g^5 \sqrt {1-c^2 x^2}}+\frac {b c^3 d^2 f x^2 \sqrt {d-c^2 d x^2}}{16 g^2 \sqrt {1-c^2 x^2}}-\frac {b c^3 d^2 f \left (c^2 f^2-2 g^2\right ) x^2 \sqrt {d-c^2 d x^2}}{4 g^4 \sqrt {1-c^2 x^2}}-\frac {b c^3 d^2 x^3 \sqrt {d-c^2 d x^2}}{45 g \sqrt {1-c^2 x^2}}+\frac {b c^3 d^2 \left (c^2 f^2-2 g^2\right ) x^3 \sqrt {d-c^2 d x^2}}{9 g^3 \sqrt {1-c^2 x^2}}-\frac {b c^5 d^2 f x^4 \sqrt {d-c^2 d x^2}}{16 g^2 \sqrt {1-c^2 x^2}}+\frac {b c^5 d^2 x^5 \sqrt {d-c^2 d x^2}}{25 g \sqrt {1-c^2 x^2}}+\frac {b d^2 \left (c^2 f^2-g^2\right )^2 \sqrt {d-c^2 d x^2} \arccos (c x)}{g^5}+\frac {c^2 d^2 f x \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{8 g^2}-\frac {c^2 d^2 f \left (c^2 f^2-2 g^2\right ) x \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{2 g^4}-\frac {c^4 d^2 f x^3 \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{4 g^2}-\frac {d^2 \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{3 g}-\frac {d^2 \left (c^2 f^2-2 g^2\right ) \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{3 g^3}+\frac {d^2 \left (1-c^2 x^2\right )^2 \sqrt {d-c^2 d x^2} (a+b \arccos (c x))}{5 g}+\frac {c d^2 f \sqrt {d-c^2 d x^2} (a+b \arccos (c x))^2}{16 b g^2 \sqrt {1-c^2 x^2}}+\frac {c d^2 f \left (c^2 f^2-2 g^2\right ) \sqrt {d-c^2 d x^2} (a+b \arccos (c x))^2}{4 b g^4 \sqrt {1-c^2 x^2}}-\frac {c d^2 \left (c^2 f^2-g^2\right )^2 x \sqrt {d-c^2 d x^2} (a+b \arccos (c x))^2}{2 b g^5 \sqrt {1-c^2 x^2}}-\frac {d^2 \left (c^2 f^2-g^2\right )^3 \sqrt {d-c^2 d x^2} (a+b \arccos (c x))^2}{2 b c g^6 (f+g x) \sqrt {1-c^2 x^2}}-\frac {d^2 \left (c^2 f^2-g^2\right )^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} (a+b \arccos (c x))^2}{2 b c g^4 (f+g x)}-\frac {a d^2 \left (c^2 f^2-g^2\right )^{5/2} \sqrt {d-c^2 d x^2} \arctan \left (\frac {g+c^2 f x}{\sqrt {c^2 f^2-g^2} \sqrt {1-c^2 x^2}}\right )}{g^6 \sqrt {1-c^2 x^2}}-\frac {i b d^2 \left (c^2 f^2-g^2\right )^{5/2} \sqrt {d-c^2 d x^2} \arccos (c x) \log \left (1+\frac {e^{i \arccos (c x)} g}{c f-\sqrt {c^2 f^2-g^2}}\right )}{g^6 \sqrt {1-c^2 x^2}}+\frac {i b d^2 \left (c^2 f^2-g^2\right )^{5/2} \sqrt {d-c^2 d x^2} \arccos (c x) \log \left (1+\frac {e^{i \arccos (c x)} g}{c f+\sqrt {c^2 f^2-g^2}}\right )}{g^6 \sqrt {1-c^2 x^2}}-\frac {b d^2 \left (c^2 f^2-g^2\right )^{5/2} \sqrt {d-c^2 d x^2} \operatorname {PolyLog}\left (2,-\frac {e^{i \arccos (c x)} g}{c f-\sqrt {c^2 f^2-g^2}}\right )}{g^6 \sqrt {1-c^2 x^2}}+\frac {b d^2 \left (c^2 f^2-g^2\right )^{5/2} \sqrt {d-c^2 d x^2} \operatorname {PolyLog}\left (2,-\frac {e^{i \arccos (c x)} g}{c f+\sqrt {c^2 f^2-g^2}}\right )}{g^6 \sqrt {1-c^2 x^2}} \]
1/25*b*c^5*d^2*x^5*(-c^2*d*x^2+d)^(1/2)/g/(-c^2*x^2+1)^(1/2)-2/15*b*c*d^2* x*(-c^2*d*x^2+d)^(1/2)/g/(-c^2*x^2+1)^(1/2)-1/45*b*c^3*d^2*x^3*(-c^2*d*x^2 +d)^(1/2)/g/(-c^2*x^2+1)^(1/2)+a*d^2*(c^2*f^2-g^2)^2*(-c^2*d*x^2+d)^(1/2)/ g^5+b*c*d^2*(c^2*f^2-g^2)^2*x*(-c^2*d*x^2+d)^(1/2)/g^5/(-c^2*x^2+1)^(1/2)- a*d^2*(c^2*f^2-g^2)^(5/2)*arctan((c^2*f*x+g)/(c^2*f^2-g^2)^(1/2)/(-c^2*x^2 +1)^(1/2))*(-c^2*d*x^2+d)^(1/2)/g^6/(-c^2*x^2+1)^(1/2)-b*d^2*(c^2*f^2-g^2) ^(5/2)*polylog(2,-(c*x+I*(-c^2*x^2+1)^(1/2))*g/(c*f-(c^2*f^2-g^2)^(1/2)))* (-c^2*d*x^2+d)^(1/2)/g^6/(-c^2*x^2+1)^(1/2)+b*d^2*(c^2*f^2-g^2)^(5/2)*poly log(2,-(c*x+I*(-c^2*x^2+1)^(1/2))*g/(c*f+(c^2*f^2-g^2)^(1/2)))*(-c^2*d*x^2 +d)^(1/2)/g^6/(-c^2*x^2+1)^(1/2)+I*b*d^2*(c^2*f^2-g^2)^(5/2)*arccos(c*x)*l n(1+(c*x+I*(-c^2*x^2+1)^(1/2))*g/(c*f+(c^2*f^2-g^2)^(1/2)))*(-c^2*d*x^2+d) ^(1/2)/g^6/(-c^2*x^2+1)^(1/2)+1/4*c*d^2*f*(c^2*f^2-2*g^2)*(a+b*arccos(c*x) )^2*(-c^2*d*x^2+d)^(1/2)/b/g^4/(-c^2*x^2+1)^(1/2)-1/2*c*d^2*(c^2*f^2-g^2)^ 2*x*(a+b*arccos(c*x))^2*(-c^2*d*x^2+d)^(1/2)/b/g^5/(-c^2*x^2+1)^(1/2)-1/2* d^2*(c^2*f^2-g^2)^3*(a+b*arccos(c*x))^2*(-c^2*d*x^2+d)^(1/2)/b/c/g^6/(g*x+ f)/(-c^2*x^2+1)^(1/2)-1/2*d^2*(c^2*f^2-g^2)^2*(a+b*arccos(c*x))^2*(-c^2*x^ 2+1)^(1/2)*(-c^2*d*x^2+d)^(1/2)/b/c/g^4/(g*x+f)-I*b*d^2*(c^2*f^2-g^2)^(5/2 )*arccos(c*x)*ln(1+(c*x+I*(-c^2*x^2+1)^(1/2))*g/(c*f-(c^2*f^2-g^2)^(1/2))) *(-c^2*d*x^2+d)^(1/2)/g^6/(-c^2*x^2+1)^(1/2)+1/8*c^2*d^2*f*x*(a+b*arccos(c *x))*(-c^2*d*x^2+d)^(1/2)/g^2-1/4*c^4*d^2*f*x^3*(a+b*arccos(c*x))*(-c^2...
Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(6216\) vs. \(2(1637)=3274\).
Time = 23.59 (sec) , antiderivative size = 6216, normalized size of antiderivative = 3.80 \[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\text {Result too large to show} \]
Time = 2.86 (sec) , antiderivative size = 1008, normalized size of antiderivative = 0.62, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {5277, 5267, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx\) |
| \(\Big \downarrow \) 5277 |
| \(\displaystyle \frac {d^2 \sqrt {d-c^2 d x^2} \int \frac {\left (1-c^2 x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x}dx}{\sqrt {1-c^2 x^2}}\) |
| \(\Big \downarrow \) 5267 |
| \(\displaystyle \frac {d^2 \sqrt {d-c^2 d x^2} \int \left (\frac {x^3 \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^4}{g}-\frac {f x^2 \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^4}{g^2}-\frac {f \left (c^2 f^2-2 g^2\right ) \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^2}{g^4}+\frac {\left (c^2 f^2-2 g^2\right ) x \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^2}{g^3}+\frac {\left (g^2-c^2 f^2\right )^2 \sqrt {1-c^2 x^2} (a+b \arccos (c x))}{g^4 (f+g x)}\right )dx}{\sqrt {1-c^2 x^2}}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {d^2 \sqrt {d-c^2 d x^2} \left (\frac {b x^5 c^5}{25 g}-\frac {b f x^4 c^5}{16 g^2}-\frac {f x^3 \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^4}{4 g^2}+\frac {b \left (c^2 f^2-2 g^2\right ) x^3 c^3}{9 g^3}-\frac {b x^3 c^3}{45 g}-\frac {b f \left (c^2 f^2-2 g^2\right ) x^2 c^3}{4 g^4}+\frac {b f x^2 c^3}{16 g^2}-\frac {f \left (c^2 f^2-2 g^2\right ) x \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^2}{2 g^4}+\frac {f x \sqrt {1-c^2 x^2} (a+b \arccos (c x)) c^2}{8 g^2}+\frac {f \left (c^2 f^2-2 g^2\right ) (a+b \arccos (c x))^2 c}{4 b g^4}-\frac {\left (c^2 f^2-g^2\right )^2 x (a+b \arccos (c x))^2 c}{2 b g^5}+\frac {f (a+b \arccos (c x))^2 c}{16 b g^2}+\frac {b \left (c^2 f^2-g^2\right )^2 x c}{g^5}-\frac {b \left (c^2 f^2-2 g^2\right ) x c}{3 g^3}-\frac {2 b x c}{15 g}+\frac {b \left (c^2 f^2-g^2\right )^2 \sqrt {1-c^2 x^2} \arccos (c x)}{g^5}+\frac {\left (1-c^2 x^2\right )^{5/2} (a+b \arccos (c x))}{5 g}-\frac {\left (c^2 f^2-2 g^2\right ) \left (1-c^2 x^2\right )^{3/2} (a+b \arccos (c x))}{3 g^3}-\frac {\left (1-c^2 x^2\right )^{3/2} (a+b \arccos (c x))}{3 g}-\frac {a \left (c^2 f^2-g^2\right )^{5/2} \arctan \left (\frac {f x c^2+g}{\sqrt {c^2 f^2-g^2} \sqrt {1-c^2 x^2}}\right )}{g^6}-\frac {i b \left (c^2 f^2-g^2\right )^{5/2} \arccos (c x) \log \left (\frac {e^{i \arccos (c x)} g}{c f-\sqrt {c^2 f^2-g^2}}+1\right )}{g^6}+\frac {i b \left (c^2 f^2-g^2\right )^{5/2} \arccos (c x) \log \left (\frac {e^{i \arccos (c x)} g}{c f+\sqrt {c^2 f^2-g^2}}+1\right )}{g^6}-\frac {b \left (c^2 f^2-g^2\right )^{5/2} \operatorname {PolyLog}\left (2,-\frac {e^{i \arccos (c x)} g}{c f-\sqrt {c^2 f^2-g^2}}\right )}{g^6}+\frac {b \left (c^2 f^2-g^2\right )^{5/2} \operatorname {PolyLog}\left (2,-\frac {e^{i \arccos (c x)} g}{c f+\sqrt {c^2 f^2-g^2}}\right )}{g^6}+\frac {a \left (c^2 f^2-g^2\right )^2 \sqrt {1-c^2 x^2}}{g^5}-\frac {\left (c^2 f^2-g^2\right )^2 \left (1-c^2 x^2\right ) (a+b \arccos (c x))^2}{2 b g^4 (f+g x) c}-\frac {\left (c^2 f^2-g^2\right )^3 (a+b \arccos (c x))^2}{2 b g^6 (f+g x) c}\right )}{\sqrt {1-c^2 x^2}}\) |
(d^2*Sqrt[d - c^2*d*x^2]*((-2*b*c*x)/(15*g) - (b*c*(c^2*f^2 - 2*g^2)*x)/(3 *g^3) + (b*c*(c^2*f^2 - g^2)^2*x)/g^5 + (b*c^3*f*x^2)/(16*g^2) - (b*c^3*f* (c^2*f^2 - 2*g^2)*x^2)/(4*g^4) - (b*c^3*x^3)/(45*g) + (b*c^3*(c^2*f^2 - 2* g^2)*x^3)/(9*g^3) - (b*c^5*f*x^4)/(16*g^2) + (b*c^5*x^5)/(25*g) + (a*(c^2* f^2 - g^2)^2*Sqrt[1 - c^2*x^2])/g^5 + (b*(c^2*f^2 - g^2)^2*Sqrt[1 - c^2*x^ 2]*ArcCos[c*x])/g^5 + (c^2*f*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(8*g ^2) - (c^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(2 *g^4) - (c^4*f*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(4*g^2) - ((1 - c^2*x^2)^(3/2)*(a + b*ArcCos[c*x]))/(3*g) - ((c^2*f^2 - 2*g^2)*(1 - c^2*x^ 2)^(3/2)*(a + b*ArcCos[c*x]))/(3*g^3) + ((1 - c^2*x^2)^(5/2)*(a + b*ArcCos [c*x]))/(5*g) + (c*f*(a + b*ArcCos[c*x])^2)/(16*b*g^2) + (c*f*(c^2*f^2 - 2 *g^2)*(a + b*ArcCos[c*x])^2)/(4*b*g^4) - (c*(c^2*f^2 - g^2)^2*x*(a + b*Arc Cos[c*x])^2)/(2*b*g^5) - ((c^2*f^2 - g^2)^3*(a + b*ArcCos[c*x])^2)/(2*b*c* g^6*(f + g*x)) - ((c^2*f^2 - g^2)^2*(1 - c^2*x^2)*(a + b*ArcCos[c*x])^2)/( 2*b*c*g^4*(f + g*x)) - (a*(c^2*f^2 - g^2)^(5/2)*ArcTan[(g + c^2*f*x)/(Sqrt [c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/g^6 - (I*b*(c^2*f^2 - g^2)^(5/2)*ArcC os[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/g^6 + (I*b*(c^2*f^2 - g^2)^(5/2)*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/g^6 - (b*(c^2*f^2 - g^2)^(5/2)*PolyLog[2, -((E^(I *ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/g^6 + (b*(c^2*f^2 - g^2...
3.1.13.3.1 Defintions of rubi rules used
Int[((a_.) + ArcCos[(c_.)*(x_)]*(b_.))^(n_.)*((f_) + (g_.)*(x_))^(m_.)*((d_ ) + (e_.)*(x_)^2)^(p_), x_Symbol] :> Int[ExpandIntegrand[Sqrt[d + e*x^2]*(a + b*ArcCos[c*x])^n, (f + g*x)^m*(d + e*x^2)^(p - 1/2), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && EqQ[c^2*d + e, 0] && IntegerQ[m] && IGtQ[p + 1/2, 0] && GtQ[d, 0] && IGtQ[n, 0]
Int[((a_.) + ArcCos[(c_.)*(x_)]*(b_.))^(n_.)*((f_) + (g_.)*(x_))^(m_.)*((d_ ) + (e_.)*(x_)^2)^(p_), x_Symbol] :> Simp[Simp[(d + e*x^2)^p/(1 - c^2*x^2)^ p] Int[(f + g*x)^m*(1 - c^2*x^2)^p*(a + b*ArcCos[c*x])^n, x], x] /; FreeQ [{a, b, c, d, e, f, g, n}, x] && EqQ[c^2*d + e, 0] && IntegerQ[m] && Intege rQ[p - 1/2] && !GtQ[d, 0]
Time = 3.12 (sec) , antiderivative size = 2665, normalized size of antiderivative = 1.63
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(2665\) |
| parts | \(\text {Expression too large to display}\) | \(2665\) |
a/g*(1/5*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(5/2)+ c^2*d*f/g*(-1/8*(-2*(x+f/g)*c^2*d+2*c^2*d*f/g)/c^2/d*(-(x+f/g)^2*c^2*d+2*c ^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)-3/16*(4*c^2*d^2*(c^2*f^2-g^2)/ g^2-4*c^4*d^2*f^2/g^2)/c^2/d*(-1/4*(-2*(x+f/g)*c^2*d+2*c^2*d*f/g)/c^2/d*(- (x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-1/8*(4*c^2* d^2*(c^2*f^2-g^2)/g^2-4*c^4*d^2*f^2/g^2)/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d )^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2) )))-d*(c^2*f^2-g^2)/g^2*(1/3*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2* f^2-g^2)/g^2)^(3/2)+c^2*d*f/g*(-1/4*(-2*(x+f/g)*c^2*d+2*c^2*d*f/g)/c^2/d*( -(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-1/8*(4*c^2 *d^2*(c^2*f^2-g^2)/g^2-4*c^4*d^2*f^2/g^2)/c^2/d/(c^2*d)^(1/2)*arctan((c^2* d)^(1/2)*x/(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2 )))-d*(c^2*f^2-g^2)/g^2*((-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2- g^2)/g^2)^(1/2)+c^2*d*f/g/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-(x+f/g)^2 *c^2*d+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+d*(c^2*f^2-g^2)/g^2 /(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/ g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-(x+f/g)^2*c^2*d+2*c^2*d*f/g*(x+f/g)-d* (c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g)))))+b*(1/16*(-d*(c^2*x^2-1))^(1/2)*(-c^2 *x^2+1)^(1/2)/(c^2*x^2-1)*arccos(c*x)^2*f*(8*c^4*f^4-20*c^2*f^2*g^2+15*g^4 )*c*d^2/g^6+1/800*(-d*(c^2*x^2-1))^(1/2)*(16*I*c^5*x^5*(-c^2*x^2+1)^(1/...
\[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\int { \frac {{\left (-c^{2} d x^{2} + d\right )}^{\frac {5}{2}} {\left (b \arccos \left (c x\right ) + a\right )}}{g x + f} \,d x } \]
integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c ^2*d^2*x^2 + b*d^2)*arccos(c*x))*sqrt(-c^2*d*x^2 + d)/(g*x + f), x)
\[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\int \frac {\left (- d \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {5}{2}} \left (a + b \operatorname {acos}{\left (c x \right )}\right )}{f + g x}\, dx \]
Exception generated. \[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\text {Exception raised: ValueError} \]
Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(g-c*f>0)', see `assume?` for mor e details)
Exception generated. \[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\text {Exception raised: TypeError} \]
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value
Timed out. \[ \int \frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \arccos (c x))}{f+g x} \, dx=\int \frac {\left (a+b\,\mathrm {acos}\left (c\,x\right )\right )\,{\left (d-c^2\,d\,x^2\right )}^{5/2}}{f+g\,x} \,d x \]