Optimal. Leaf size=343 \[ -\frac {32 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{45045 c^5 e^2 (d+e x)^{7/2}}-\frac {16 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac {4 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{715 c^3 e^2 (d+e x)^{3/2}}-\frac {2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{195 c^2 e^2 \sqrt {d+e x}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.57, antiderivative size = 343, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {794, 656, 648} \begin {gather*} -\frac {2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{195 c^2 e^2 \sqrt {d+e x}}-\frac {4 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{715 c^3 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac {32 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-8 b e g+c d g+15 c e f)}{45045 c^5 e^2 (d+e x)^{7/2}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 648
Rule 656
Rule 794
Rubi steps
\begin {align*} \int \sqrt {d+e x} (f+g x) \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx &=-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2}-\frac {\left (2 \left (\frac {7}{2} e \left (-2 c e^2 f+b e^2 g\right )+\frac {1}{2} \left (-c e^3 f+\left (-c d e^2+b e^3\right ) g\right )\right )\right ) \int \sqrt {d+e x} \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx}{15 c e^3}\\ &=-\frac {2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{195 c^2 e^2 \sqrt {d+e x}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2}+\frac {(2 (2 c d-b e) (15 c e f+c d g-8 b e g)) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{\sqrt {d+e x}} \, dx}{65 c^2 e}\\ &=-\frac {4 (2 c d-b e) (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{715 c^3 e^2 (d+e x)^{3/2}}-\frac {2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{195 c^2 e^2 \sqrt {d+e x}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2}+\frac {\left (8 (2 c d-b e)^2 (15 c e f+c d g-8 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{3/2}} \, dx}{715 c^3 e}\\ &=-\frac {16 (2 c d-b e)^2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac {4 (2 c d-b e) (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{715 c^3 e^2 (d+e x)^{3/2}}-\frac {2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{195 c^2 e^2 \sqrt {d+e x}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2}+\frac {\left (16 (2 c d-b e)^3 (15 c e f+c d g-8 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{5/2}} \, dx}{6435 c^4 e}\\ &=-\frac {32 (2 c d-b e)^3 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{45045 c^5 e^2 (d+e x)^{7/2}}-\frac {16 (2 c d-b e)^2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac {4 (2 c d-b e) (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{715 c^3 e^2 (d+e x)^{3/2}}-\frac {2 (15 c e f+c d g-8 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{195 c^2 e^2 \sqrt {d+e x}}-\frac {2 g \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{15 c e^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.29, size = 264, normalized size = 0.77 \begin {gather*} \frac {2 (b e-c d+c e x)^3 \sqrt {(d+e x) (c (d-e x)-b e)} \left (128 b^4 e^4 g-16 b^3 c e^3 (77 d g+15 e f+28 e g x)+24 b^2 c^2 e^2 \left (187 d^2 g+d e (95 f+161 g x)+7 e^2 x (5 f+6 g x)\right )-2 b c^3 e \left (3611 d^3 g+d^2 e (4065 f+5922 g x)+21 d e^2 x (170 f+183 g x)+21 e^3 x^2 (45 f+44 g x)\right )+c^4 \left (3838 d^4 g+d^3 e (12525 f+13433 g x)+147 d^2 e^2 x (145 f+129 g x)+21 d e^3 x^2 (675 f+583 g x)+231 e^4 x^3 (15 f+13 g x)\right )\right )}{45045 c^5 e^2 \sqrt {d+e x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 7.43, size = 401, normalized size = 1.17 \begin {gather*} -\frac {2 \left ((d+e x) (2 c d-b e)-c (d+e x)^2\right )^{7/2} \left (128 b^4 e^4 g-448 b^3 c e^3 g (d+e x)-784 b^3 c d e^3 g-240 b^3 c e^4 f+1632 b^2 c^2 d^2 e^2 g+840 b^2 c^2 e^3 f (d+e x)+1440 b^2 c^2 d e^3 f+1008 b^2 c^2 e^2 g (d+e x)^2+1848 b^2 c^2 d e^2 g (d+e x)-1216 b c^3 d^3 e g-2880 b c^3 d^2 e^2 f-2016 b c^3 d^2 e g (d+e x)-1890 b c^3 e^2 f (d+e x)^2-3360 b c^3 d e^2 f (d+e x)-1848 b c^3 e g (d+e x)^3-2142 b c^3 d e g (d+e x)^2+128 c^4 d^4 g+1920 c^4 d^3 e f+224 c^4 d^3 g (d+e x)+3360 c^4 d^2 e f (d+e x)+252 c^4 d^2 g (d+e x)^2+3465 c^4 e f (d+e x)^3+3780 c^4 d e f (d+e x)^2+3003 c^4 g (d+e x)^4+231 c^4 d g (d+e x)^3\right )}{45045 c^5 e^2 (d+e x)^{7/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.43, size = 881, normalized size = 2.57 \begin {gather*} \frac {2 \, {\left (3003 \, c^{7} e^{7} g x^{7} + 231 \, {\left (15 \, c^{7} e^{7} f + {\left (14 \, c^{7} d e^{6} + 31 \, b c^{6} e^{7}\right )} g\right )} x^{6} + 63 \, {\left (15 \, {\left (4 \, c^{7} d e^{6} + 9 \, b c^{6} e^{7}\right )} f - {\left (139 \, c^{7} d^{2} e^{5} - 263 \, b c^{6} d e^{6} - 71 \, b^{2} c^{5} e^{7}\right )} g\right )} x^{5} - 35 \, {\left (3 \, {\left (103 \, c^{7} d^{2} e^{5} - 193 \, b c^{6} d e^{6} - 53 \, b^{2} c^{5} e^{7}\right )} f + {\left (278 \, c^{7} d^{3} e^{4} + 54 \, b c^{6} d^{2} e^{5} - 474 \, b^{2} c^{5} d e^{6} - b^{3} c^{4} e^{7}\right )} g\right )} x^{4} - 5 \, {\left (3 \, {\left (824 \, c^{7} d^{3} e^{4} + 206 \, b c^{6} d^{2} e^{5} - 1454 \, b^{2} c^{5} d e^{6} - 5 \, b^{3} c^{4} e^{7}\right )} f - {\left (1637 \, c^{7} d^{4} e^{3} - 5930 \, b c^{6} d^{3} e^{4} + 4224 \, b^{2} c^{5} d^{2} e^{5} + 77 \, b^{3} c^{4} d e^{6} - 8 \, b^{4} c^{3} e^{7}\right )} g\right )} x^{3} + 3 \, {\left (15 \, {\left (271 \, c^{7} d^{4} e^{3} - 954 \, b c^{6} d^{3} e^{4} + 664 \, b^{2} c^{5} d^{2} e^{5} + 21 \, b^{3} c^{4} d e^{6} - 2 \, b^{4} c^{3} e^{7}\right )} f + {\left (3274 \, c^{7} d^{5} e^{2} - 6125 \, b c^{6} d^{4} e^{3} + 2290 \, b^{2} c^{5} d^{3} e^{4} + 715 \, b^{3} c^{4} d^{2} e^{5} - 170 \, b^{4} c^{3} d e^{6} + 16 \, b^{5} c^{2} e^{7}\right )} g\right )} x^{2} - 15 \, {\left (835 \, c^{7} d^{6} e - 3047 \, b c^{6} d^{5} e^{2} + 4283 \, b^{2} c^{5} d^{4} e^{3} - 2933 \, b^{3} c^{4} d^{3} e^{4} + 1046 \, b^{4} c^{3} d^{2} e^{5} - 200 \, b^{5} c^{2} d e^{6} + 16 \, b^{6} c e^{7}\right )} f - 2 \, {\left (1919 \, c^{7} d^{7} - 9368 \, b c^{6} d^{6} e + 18834 \, b^{2} c^{5} d^{5} e^{2} - 20100 \, b^{3} c^{4} d^{4} e^{3} + 12255 \, b^{4} c^{3} d^{3} e^{4} - 4284 \, b^{5} c^{2} d^{2} e^{5} + 808 \, b^{6} c d e^{6} - 64 \, b^{7} e^{7}\right )} g + {\left (15 \, {\left (1084 \, c^{7} d^{5} e^{2} - 1897 \, b c^{6} d^{4} e^{3} + 466 \, b^{2} c^{5} d^{3} e^{4} + 431 \, b^{3} c^{4} d^{2} e^{5} - 92 \, b^{4} c^{3} d e^{6} + 8 \, b^{5} c^{2} e^{7}\right )} f - {\left (1919 \, c^{7} d^{6} e - 7449 \, b c^{6} d^{5} e^{2} + 11385 \, b^{2} c^{5} d^{4} e^{3} - 8715 \, b^{3} c^{4} d^{3} e^{4} + 3540 \, b^{4} c^{3} d^{2} e^{5} - 744 \, b^{5} c^{2} d e^{6} + 64 \, b^{6} c e^{7}\right )} g\right )} x\right )} \sqrt {-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt {e x + d}}{45045 \, {\left (c^{5} e^{3} x + c^{5} d e^{2}\right )}} \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*} \int {\left (-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right )}^{\frac {5}{2}} \sqrt {e x + d} {\left (g x + f\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 367, normalized size = 1.07 \begin {gather*} \frac {2 \left (c e x +b e -c d \right ) \left (3003 g \,e^{4} x^{4} c^{4}-1848 b \,c^{3} e^{4} g \,x^{3}+12243 c^{4} d \,e^{3} g \,x^{3}+3465 c^{4} e^{4} f \,x^{3}+1008 b^{2} c^{2} e^{4} g \,x^{2}-7686 b \,c^{3} d \,e^{3} g \,x^{2}-1890 b \,c^{3} e^{4} f \,x^{2}+18963 c^{4} d^{2} e^{2} g \,x^{2}+14175 c^{4} d \,e^{3} f \,x^{2}-448 b^{3} c \,e^{4} g x +3864 b^{2} c^{2} d \,e^{3} g x +840 b^{2} c^{2} e^{4} f x -11844 b \,c^{3} d^{2} e^{2} g x -7140 b \,c^{3} d \,e^{3} f x +13433 c^{4} d^{3} e g x +21315 c^{4} d^{2} e^{2} f x +128 b^{4} e^{4} g -1232 b^{3} c d \,e^{3} g -240 b^{3} c \,e^{4} f +4488 b^{2} c^{2} d^{2} e^{2} g +2280 b^{2} c^{2} d \,e^{3} f -7222 b \,c^{3} d^{3} e g -8130 b \,c^{3} d^{2} e^{2} f +3838 c^{4} d^{4} g +12525 f \,d^{3} c^{4} e \right ) \left (-c \,e^{2} x^{2}-b \,e^{2} x -b d e +c \,d^{2}\right )^{\frac {5}{2}}}{45045 \left (e x +d \right )^{\frac {5}{2}} c^{5} e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 1.00, size = 878, normalized size = 2.56 \begin {gather*} \frac {2 \, {\left (231 \, c^{6} e^{6} x^{6} - 835 \, c^{6} d^{6} + 3047 \, b c^{5} d^{5} e - 4283 \, b^{2} c^{4} d^{4} e^{2} + 2933 \, b^{3} c^{3} d^{3} e^{3} - 1046 \, b^{4} c^{2} d^{2} e^{4} + 200 \, b^{5} c d e^{5} - 16 \, b^{6} e^{6} + 63 \, {\left (4 \, c^{6} d e^{5} + 9 \, b c^{5} e^{6}\right )} x^{5} - 7 \, {\left (103 \, c^{6} d^{2} e^{4} - 193 \, b c^{5} d e^{5} - 53 \, b^{2} c^{4} e^{6}\right )} x^{4} - {\left (824 \, c^{6} d^{3} e^{3} + 206 \, b c^{5} d^{2} e^{4} - 1454 \, b^{2} c^{4} d e^{5} - 5 \, b^{3} c^{3} e^{6}\right )} x^{3} + 3 \, {\left (271 \, c^{6} d^{4} e^{2} - 954 \, b c^{5} d^{3} e^{3} + 664 \, b^{2} c^{4} d^{2} e^{4} + 21 \, b^{3} c^{3} d e^{5} - 2 \, b^{4} c^{2} e^{6}\right )} x^{2} + {\left (1084 \, c^{6} d^{5} e - 1897 \, b c^{5} d^{4} e^{2} + 466 \, b^{2} c^{4} d^{3} e^{3} + 431 \, b^{3} c^{3} d^{2} e^{4} - 92 \, b^{4} c^{2} d e^{5} + 8 \, b^{5} c e^{6}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} f}{3003 \, {\left (c^{4} e^{2} x + c^{4} d e\right )}} + \frac {2 \, {\left (3003 \, c^{7} e^{7} x^{7} - 3838 \, c^{7} d^{7} + 18736 \, b c^{6} d^{6} e - 37668 \, b^{2} c^{5} d^{5} e^{2} + 40200 \, b^{3} c^{4} d^{4} e^{3} - 24510 \, b^{4} c^{3} d^{3} e^{4} + 8568 \, b^{5} c^{2} d^{2} e^{5} - 1616 \, b^{6} c d e^{6} + 128 \, b^{7} e^{7} + 231 \, {\left (14 \, c^{7} d e^{6} + 31 \, b c^{6} e^{7}\right )} x^{6} - 63 \, {\left (139 \, c^{7} d^{2} e^{5} - 263 \, b c^{6} d e^{6} - 71 \, b^{2} c^{5} e^{7}\right )} x^{5} - 35 \, {\left (278 \, c^{7} d^{3} e^{4} + 54 \, b c^{6} d^{2} e^{5} - 474 \, b^{2} c^{5} d e^{6} - b^{3} c^{4} e^{7}\right )} x^{4} + 5 \, {\left (1637 \, c^{7} d^{4} e^{3} - 5930 \, b c^{6} d^{3} e^{4} + 4224 \, b^{2} c^{5} d^{2} e^{5} + 77 \, b^{3} c^{4} d e^{6} - 8 \, b^{4} c^{3} e^{7}\right )} x^{3} + 3 \, {\left (3274 \, c^{7} d^{5} e^{2} - 6125 \, b c^{6} d^{4} e^{3} + 2290 \, b^{2} c^{5} d^{3} e^{4} + 715 \, b^{3} c^{4} d^{2} e^{5} - 170 \, b^{4} c^{3} d e^{6} + 16 \, b^{5} c^{2} e^{7}\right )} x^{2} - {\left (1919 \, c^{7} d^{6} e - 7449 \, b c^{6} d^{5} e^{2} + 11385 \, b^{2} c^{5} d^{4} e^{3} - 8715 \, b^{3} c^{4} d^{3} e^{4} + 3540 \, b^{4} c^{3} d^{2} e^{5} - 744 \, b^{5} c^{2} d e^{6} + 64 \, b^{6} c e^{7}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} g}{45045 \, {\left (c^{5} e^{3} x + c^{5} d e^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.03, size = 769, normalized size = 2.24 \begin {gather*} \frac {\sqrt {c\,d^2-b\,d\,e-c\,e^2\,x^2-b\,e^2\,x}\,\left (\frac {2\,e^2\,x^5\,\sqrt {d+e\,x}\,\left (71\,g\,b^2\,e^2+263\,g\,b\,c\,d\,e+135\,f\,b\,c\,e^2-139\,g\,c^2\,d^2+60\,f\,c^2\,d\,e\right )}{715}+\frac {x^3\,\sqrt {d+e\,x}\,\left (-80\,g\,b^4\,c^3\,e^7+770\,g\,b^3\,c^4\,d\,e^6+150\,f\,b^3\,c^4\,e^7+42240\,g\,b^2\,c^5\,d^2\,e^5+43620\,f\,b^2\,c^5\,d\,e^6-59300\,g\,b\,c^6\,d^3\,e^4-6180\,f\,b\,c^6\,d^2\,e^5+16370\,g\,c^7\,d^4\,e^3-24720\,f\,c^7\,d^3\,e^4\right )}{45045\,c^5\,e^3}+\frac {2\,c^2\,e^4\,g\,x^7\,\sqrt {d+e\,x}}{15}+\frac {2\,{\left (b\,e-c\,d\right )}^3\,\sqrt {d+e\,x}\,\left (128\,g\,b^4\,e^4-1232\,g\,b^3\,c\,d\,e^3-240\,f\,b^3\,c\,e^4+4488\,g\,b^2\,c^2\,d^2\,e^2+2280\,f\,b^2\,c^2\,d\,e^3-7222\,g\,b\,c^3\,d^3\,e-8130\,f\,b\,c^3\,d^2\,e^2+3838\,g\,c^4\,d^4+12525\,f\,c^4\,d^3\,e\right )}{45045\,c^5\,e^3}+\frac {x^4\,\sqrt {d+e\,x}\,\left (70\,g\,b^3\,c^4\,e^7+33180\,g\,b^2\,c^5\,d\,e^6+11130\,f\,b^2\,c^5\,e^7-3780\,g\,b\,c^6\,d^2\,e^5+40530\,f\,b\,c^6\,d\,e^6-19460\,g\,c^7\,d^3\,e^4-21630\,f\,c^7\,d^2\,e^5\right )}{45045\,c^5\,e^3}+\frac {2\,c\,e^3\,x^6\,\sqrt {d+e\,x}\,\left (31\,b\,e\,g+14\,c\,d\,g+15\,c\,e\,f\right )}{195}+\frac {2\,x^2\,\left (b\,e-c\,d\right )\,\sqrt {d+e\,x}\,\left (16\,g\,b^4\,e^4-154\,g\,b^3\,c\,d\,e^3-30\,f\,b^3\,c\,e^4+561\,g\,b^2\,c^2\,d^2\,e^2+285\,f\,b^2\,c^2\,d\,e^3+2851\,g\,b\,c^3\,d^3\,e+10245\,f\,b\,c^3\,d^2\,e^2-3274\,g\,c^4\,d^4-4065\,f\,c^4\,d^3\,e\right )}{15015\,c^3\,e}+\frac {2\,x\,{\left (b\,e-c\,d\right )}^2\,\sqrt {d+e\,x}\,\left (-64\,g\,b^4\,e^4+616\,g\,b^3\,c\,d\,e^3+120\,f\,b^3\,c\,e^4-2244\,g\,b^2\,c^2\,d^2\,e^2-1140\,f\,b^2\,c^2\,d\,e^3+3611\,g\,b\,c^3\,d^3\,e+4065\,f\,b\,c^3\,d^2\,e^2-1919\,g\,c^4\,d^4+16260\,f\,c^4\,d^3\,e\right )}{45045\,c^4\,e^2}\right )}{x+\frac {d}{e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (- \left (d + e x\right ) \left (b e - c d + c e x\right )\right )^{\frac {5}{2}} \sqrt {d + e x} \left (f + g x\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________