3.2.64 \(\int \frac {(a+b x)^{10} (A+B x)}{x^{17}} \, dx\) [164]

Optimal. Leaf size=159 \[ -\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}-\frac {b (5 A b-16 a B) (a+b x)^{11}}{840 a^3 x^{14}}+\frac {b^2 (5 A b-16 a B) (a+b x)^{11}}{3640 a^4 x^{13}}-\frac {b^3 (5 A b-16 a B) (a+b x)^{11}}{21840 a^5 x^{12}}+\frac {b^4 (5 A b-16 a B) (a+b x)^{11}}{240240 a^6 x^{11}} \]

[Out]

-1/16*A*(b*x+a)^11/a/x^16+1/240*(5*A*b-16*B*a)*(b*x+a)^11/a^2/x^15-1/840*b*(5*A*b-16*B*a)*(b*x+a)^11/a^3/x^14+
1/3640*b^2*(5*A*b-16*B*a)*(b*x+a)^11/a^4/x^13-1/21840*b^3*(5*A*b-16*B*a)*(b*x+a)^11/a^5/x^12+1/240240*b^4*(5*A
*b-16*B*a)*(b*x+a)^11/a^6/x^11

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Rubi [A]
time = 0.04, antiderivative size = 159, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {79, 47, 37} \begin {gather*} \frac {b^4 (a+b x)^{11} (5 A b-16 a B)}{240240 a^6 x^{11}}-\frac {b^3 (a+b x)^{11} (5 A b-16 a B)}{21840 a^5 x^{12}}+\frac {b^2 (a+b x)^{11} (5 A b-16 a B)}{3640 a^4 x^{13}}-\frac {b (a+b x)^{11} (5 A b-16 a B)}{840 a^3 x^{14}}+\frac {(a+b x)^{11} (5 A b-16 a B)}{240 a^2 x^{15}}-\frac {A (a+b x)^{11}}{16 a x^{16}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((a + b*x)^10*(A + B*x))/x^17,x]

[Out]

-1/16*(A*(a + b*x)^11)/(a*x^16) + ((5*A*b - 16*a*B)*(a + b*x)^11)/(240*a^2*x^15) - (b*(5*A*b - 16*a*B)*(a + b*
x)^11)/(840*a^3*x^14) + (b^2*(5*A*b - 16*a*B)*(a + b*x)^11)/(3640*a^4*x^13) - (b^3*(5*A*b - 16*a*B)*(a + b*x)^
11)/(21840*a^5*x^12) + (b^4*(5*A*b - 16*a*B)*(a + b*x)^11)/(240240*a^6*x^11)

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[(a + b*x)^(m + 1)*((c + d*x)^(n +
1)/((b*c - a*d)*(m + 1))), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rule 47

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[(a + b*x)^(m + 1)*((c + d*x)^(n + 1
)/((b*c - a*d)*(m + 1))), x] - Dist[d*(Simplify[m + n + 2]/((b*c - a*d)*(m + 1))), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] &&  !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] ||  !SumSimplerQ[n, 1])

Rule 79

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(-(b*e - a*f
))*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(f*(p + 1)*(c*f - d*e))), x] - Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1
) + c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)), Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e,
f, n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || IntegerQ[p] ||  !(IntegerQ[n] ||  !(EqQ[e, 0] ||  !(EqQ[c, 0] || L
tQ[p, n]))))

Rubi steps

\begin {align*} \int \frac {(a+b x)^{10} (A+B x)}{x^{17}} \, dx &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(-5 A b+16 a B) \int \frac {(a+b x)^{10}}{x^{16}} \, dx}{16 a}\\ &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}+\frac {(b (5 A b-16 a B)) \int \frac {(a+b x)^{10}}{x^{15}} \, dx}{60 a^2}\\ &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}-\frac {b (5 A b-16 a B) (a+b x)^{11}}{840 a^3 x^{14}}-\frac {\left (b^2 (5 A b-16 a B)\right ) \int \frac {(a+b x)^{10}}{x^{14}} \, dx}{280 a^3}\\ &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}-\frac {b (5 A b-16 a B) (a+b x)^{11}}{840 a^3 x^{14}}+\frac {b^2 (5 A b-16 a B) (a+b x)^{11}}{3640 a^4 x^{13}}+\frac {\left (b^3 (5 A b-16 a B)\right ) \int \frac {(a+b x)^{10}}{x^{13}} \, dx}{1820 a^4}\\ &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}-\frac {b (5 A b-16 a B) (a+b x)^{11}}{840 a^3 x^{14}}+\frac {b^2 (5 A b-16 a B) (a+b x)^{11}}{3640 a^4 x^{13}}-\frac {b^3 (5 A b-16 a B) (a+b x)^{11}}{21840 a^5 x^{12}}-\frac {\left (b^4 (5 A b-16 a B)\right ) \int \frac {(a+b x)^{10}}{x^{12}} \, dx}{21840 a^5}\\ &=-\frac {A (a+b x)^{11}}{16 a x^{16}}+\frac {(5 A b-16 a B) (a+b x)^{11}}{240 a^2 x^{15}}-\frac {b (5 A b-16 a B) (a+b x)^{11}}{840 a^3 x^{14}}+\frac {b^2 (5 A b-16 a B) (a+b x)^{11}}{3640 a^4 x^{13}}-\frac {b^3 (5 A b-16 a B) (a+b x)^{11}}{21840 a^5 x^{12}}+\frac {b^4 (5 A b-16 a B) (a+b x)^{11}}{240240 a^6 x^{11}}\\ \end {align*}

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Mathematica [A]
time = 0.05, size = 222, normalized size = 1.40 \begin {gather*} -\frac {b^{10} (5 A+6 B x)}{30 x^6}-\frac {5 a b^9 (6 A+7 B x)}{21 x^7}-\frac {45 a^2 b^8 (7 A+8 B x)}{56 x^8}-\frac {5 a^3 b^7 (8 A+9 B x)}{3 x^9}-\frac {7 a^4 b^6 (9 A+10 B x)}{3 x^{10}}-\frac {126 a^5 b^5 (10 A+11 B x)}{55 x^{11}}-\frac {35 a^6 b^4 (11 A+12 B x)}{22 x^{12}}-\frac {10 a^7 b^3 (12 A+13 B x)}{13 x^{13}}-\frac {45 a^8 b^2 (13 A+14 B x)}{182 x^{14}}-\frac {a^9 b (14 A+15 B x)}{21 x^{15}}-\frac {a^{10} (15 A+16 B x)}{240 x^{16}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x)^10*(A + B*x))/x^17,x]

[Out]

-1/30*(b^10*(5*A + 6*B*x))/x^6 - (5*a*b^9*(6*A + 7*B*x))/(21*x^7) - (45*a^2*b^8*(7*A + 8*B*x))/(56*x^8) - (5*a
^3*b^7*(8*A + 9*B*x))/(3*x^9) - (7*a^4*b^6*(9*A + 10*B*x))/(3*x^10) - (126*a^5*b^5*(10*A + 11*B*x))/(55*x^11)
- (35*a^6*b^4*(11*A + 12*B*x))/(22*x^12) - (10*a^7*b^3*(12*A + 13*B*x))/(13*x^13) - (45*a^8*b^2*(13*A + 14*B*x
))/(182*x^14) - (a^9*b*(14*A + 15*B*x))/(21*x^15) - (a^10*(15*A + 16*B*x))/(240*x^16)

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Maple [A]
time = 0.07, size = 208, normalized size = 1.31

method	result	size
default	\(-\frac {a^{9} \left (10 A b +B a \right )}{15 x^{15}}-\frac {10 a^{3} b^{6} \left (4 A b +7 B a \right )}{3 x^{9}}-\frac {42 a^{5} b^{4} \left (6 A b +5 B a \right )}{11 x^{11}}-\frac {b^{10} B}{5 x^{5}}-\frac {5 a^{6} b^{3} \left (7 A b +4 B a \right )}{2 x^{12}}-\frac {b^{9} \left (A b +10 B a \right )}{6 x^{6}}-\frac {a^{10} A}{16 x^{16}}-\frac {21 a^{4} b^{5} \left (5 A b +6 B a \right )}{5 x^{10}}-\frac {5 a^{8} b \left (9 A b +2 B a \right )}{14 x^{14}}-\frac {15 a^{7} b^{2} \left (8 A b +3 B a \right )}{13 x^{13}}-\frac {15 a^{2} b^{7} \left (3 A b +8 B a \right )}{8 x^{8}}-\frac {5 a \,b^{8} \left (2 A b +9 B a \right )}{7 x^{7}}\)	\(208\)
norman	\(\frac {-\frac {a^{10} A}{16}+\left (-\frac {2}{3} a^{9} b A -\frac {1}{15} a^{10} B \right ) x +\left (-\frac {45}{14} a^{8} b^{2} A -\frac {5}{7} a^{9} b B \right ) x^{2}+\left (-\frac {120}{13} a^{7} b^{3} A -\frac {45}{13} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {35}{2} a^{6} b^{4} A -10 a^{7} b^{3} B \right ) x^{4}+\left (-\frac {252}{11} a^{5} b^{5} A -\frac {210}{11} a^{6} b^{4} B \right ) x^{5}+\left (-21 a^{4} b^{6} A -\frac {126}{5} a^{5} b^{5} B \right ) x^{6}+\left (-\frac {40}{3} a^{3} b^{7} A -\frac {70}{3} a^{4} b^{6} B \right ) x^{7}+\left (-\frac {45}{8} a^{2} b^{8} A -15 a^{3} b^{7} B \right ) x^{8}+\left (-\frac {10}{7} a \,b^{9} A -\frac {45}{7} a^{2} b^{8} B \right ) x^{9}+\left (-\frac {1}{6} b^{10} A -\frac {5}{3} a \,b^{9} B \right ) x^{10}-\frac {b^{10} B \,x^{11}}{5}}{x^{16}}\)	\(235\)
risch	\(\frac {-\frac {a^{10} A}{16}+\left (-\frac {2}{3} a^{9} b A -\frac {1}{15} a^{10} B \right ) x +\left (-\frac {45}{14} a^{8} b^{2} A -\frac {5}{7} a^{9} b B \right ) x^{2}+\left (-\frac {120}{13} a^{7} b^{3} A -\frac {45}{13} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {35}{2} a^{6} b^{4} A -10 a^{7} b^{3} B \right ) x^{4}+\left (-\frac {252}{11} a^{5} b^{5} A -\frac {210}{11} a^{6} b^{4} B \right ) x^{5}+\left (-21 a^{4} b^{6} A -\frac {126}{5} a^{5} b^{5} B \right ) x^{6}+\left (-\frac {40}{3} a^{3} b^{7} A -\frac {70}{3} a^{4} b^{6} B \right ) x^{7}+\left (-\frac {45}{8} a^{2} b^{8} A -15 a^{3} b^{7} B \right ) x^{8}+\left (-\frac {10}{7} a \,b^{9} A -\frac {45}{7} a^{2} b^{8} B \right ) x^{9}+\left (-\frac {1}{6} b^{10} A -\frac {5}{3} a \,b^{9} B \right ) x^{10}-\frac {b^{10} B \,x^{11}}{5}}{x^{16}}\)	\(235\)
gosper	\(-\frac {48048 b^{10} B \,x^{11}+40040 A \,b^{10} x^{10}+400400 B a \,b^{9} x^{10}+343200 a A \,b^{9} x^{9}+1544400 B \,a^{2} b^{8} x^{9}+1351350 a^{2} A \,b^{8} x^{8}+3603600 B \,a^{3} b^{7} x^{8}+3203200 a^{3} A \,b^{7} x^{7}+5605600 B \,a^{4} b^{6} x^{7}+5045040 a^{4} A \,b^{6} x^{6}+6054048 B \,a^{5} b^{5} x^{6}+5503680 a^{5} A \,b^{5} x^{5}+4586400 B \,a^{6} b^{4} x^{5}+4204200 a^{6} A \,b^{4} x^{4}+2402400 B \,a^{7} b^{3} x^{4}+2217600 a^{7} A \,b^{3} x^{3}+831600 B \,a^{8} b^{2} x^{3}+772200 a^{8} A \,b^{2} x^{2}+171600 B \,a^{9} b \,x^{2}+160160 a^{9} A b x +16016 a^{10} B x +15015 a^{10} A}{240240 x^{16}}\)	\(244\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^10*(B*x+A)/x^17,x,method=_RETURNVERBOSE)

[Out]

-1/15*a^9*(10*A*b+B*a)/x^15-10/3*a^3*b^6*(4*A*b+7*B*a)/x^9-42/11*a^5*b^4*(6*A*b+5*B*a)/x^11-1/5*b^10*B/x^5-5/2
*a^6*b^3*(7*A*b+4*B*a)/x^12-1/6*b^9*(A*b+10*B*a)/x^6-1/16*a^10*A/x^16-21/5*a^4*b^5*(5*A*b+6*B*a)/x^10-5/14*a^8
*b*(9*A*b+2*B*a)/x^14-15/13*a^7*b^2*(8*A*b+3*B*a)/x^13-15/8*a^2*b^7*(3*A*b+8*B*a)/x^8-5/7*a*b^8*(2*A*b+9*B*a)/
x^7

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Maxima [A]
time = 0.29, size = 243, normalized size = 1.53 \begin {gather*} -\frac {48048 \, B b^{10} x^{11} + 15015 \, A a^{10} + 40040 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 171600 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 450450 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 800800 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 1009008 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 917280 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 600600 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 277200 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 85800 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 16016 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{240240 \, x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/x^17,x, algorithm="maxima")

[Out]

-1/240240*(48048*B*b^10*x^11 + 15015*A*a^10 + 40040*(10*B*a*b^9 + A*b^10)*x^10 + 171600*(9*B*a^2*b^8 + 2*A*a*b
^9)*x^9 + 450450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 800800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 1009008*(6*B*a^5*b
^5 + 5*A*a^4*b^6)*x^6 + 917280*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 600600*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 2772
00*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 85800*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 16016*(B*a^10 + 10*A*a^9*b)*x)/x^16

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Fricas [A]
time = 0.51, size = 243, normalized size = 1.53 \begin {gather*} -\frac {48048 \, B b^{10} x^{11} + 15015 \, A a^{10} + 40040 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 171600 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 450450 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 800800 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 1009008 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 917280 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 600600 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 277200 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 85800 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 16016 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{240240 \, x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/x^17,x, algorithm="fricas")

[Out]

-1/240240*(48048*B*b^10*x^11 + 15015*A*a^10 + 40040*(10*B*a*b^9 + A*b^10)*x^10 + 171600*(9*B*a^2*b^8 + 2*A*a*b
^9)*x^9 + 450450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 800800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 1009008*(6*B*a^5*b
^5 + 5*A*a^4*b^6)*x^6 + 917280*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 600600*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 2772
00*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 85800*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 16016*(B*a^10 + 10*A*a^9*b)*x)/x^16

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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]

integrate((b*x+a)**10*(B*x+A)/x**17,x)

[Out]

Timed out

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Giac [A]
time = 2.93, size = 243, normalized size = 1.53 \begin {gather*} -\frac {48048 \, B b^{10} x^{11} + 400400 \, B a b^{9} x^{10} + 40040 \, A b^{10} x^{10} + 1544400 \, B a^{2} b^{8} x^{9} + 343200 \, A a b^{9} x^{9} + 3603600 \, B a^{3} b^{7} x^{8} + 1351350 \, A a^{2} b^{8} x^{8} + 5605600 \, B a^{4} b^{6} x^{7} + 3203200 \, A a^{3} b^{7} x^{7} + 6054048 \, B a^{5} b^{5} x^{6} + 5045040 \, A a^{4} b^{6} x^{6} + 4586400 \, B a^{6} b^{4} x^{5} + 5503680 \, A a^{5} b^{5} x^{5} + 2402400 \, B a^{7} b^{3} x^{4} + 4204200 \, A a^{6} b^{4} x^{4} + 831600 \, B a^{8} b^{2} x^{3} + 2217600 \, A a^{7} b^{3} x^{3} + 171600 \, B a^{9} b x^{2} + 772200 \, A a^{8} b^{2} x^{2} + 16016 \, B a^{10} x + 160160 \, A a^{9} b x + 15015 \, A a^{10}}{240240 \, x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^10*(B*x+A)/x^17,x, algorithm="giac")

[Out]

-1/240240*(48048*B*b^10*x^11 + 400400*B*a*b^9*x^10 + 40040*A*b^10*x^10 + 1544400*B*a^2*b^8*x^9 + 343200*A*a*b^
9*x^9 + 3603600*B*a^3*b^7*x^8 + 1351350*A*a^2*b^8*x^8 + 5605600*B*a^4*b^6*x^7 + 3203200*A*a^3*b^7*x^7 + 605404
8*B*a^5*b^5*x^6 + 5045040*A*a^4*b^6*x^6 + 4586400*B*a^6*b^4*x^5 + 5503680*A*a^5*b^5*x^5 + 2402400*B*a^7*b^3*x^
4 + 4204200*A*a^6*b^4*x^4 + 831600*B*a^8*b^2*x^3 + 2217600*A*a^7*b^3*x^3 + 171600*B*a^9*b*x^2 + 772200*A*a^8*b
^2*x^2 + 16016*B*a^10*x + 160160*A*a^9*b*x + 15015*A*a^10)/x^16

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Mupad [B]
time = 0.39, size = 235, normalized size = 1.48 \begin {gather*} -\frac {x\,\left (\frac {B\,a^{10}}{15}+\frac {2\,A\,b\,a^9}{3}\right )+\frac {A\,a^{10}}{16}+x^2\,\left (\frac {5\,B\,a^9\,b}{7}+\frac {45\,A\,a^8\,b^2}{14}\right )+x^9\,\left (\frac {45\,B\,a^2\,b^8}{7}+\frac {10\,A\,a\,b^9}{7}\right )+x^{10}\,\left (\frac {A\,b^{10}}{6}+\frac {5\,B\,a\,b^9}{3}\right )+x^4\,\left (10\,B\,a^7\,b^3+\frac {35\,A\,a^6\,b^4}{2}\right )+x^8\,\left (15\,B\,a^3\,b^7+\frac {45\,A\,a^2\,b^8}{8}\right )+x^7\,\left (\frac {70\,B\,a^4\,b^6}{3}+\frac {40\,A\,a^3\,b^7}{3}\right )+x^6\,\left (\frac {126\,B\,a^5\,b^5}{5}+21\,A\,a^4\,b^6\right )+x^3\,\left (\frac {45\,B\,a^8\,b^2}{13}+\frac {120\,A\,a^7\,b^3}{13}\right )+x^5\,\left (\frac {210\,B\,a^6\,b^4}{11}+\frac {252\,A\,a^5\,b^5}{11}\right )+\frac {B\,b^{10}\,x^{11}}{5}}{x^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((A + B*x)*(a + b*x)^10)/x^17,x)

[Out]

-(x*((B*a^10)/15 + (2*A*a^9*b)/3) + (A*a^10)/16 + x^2*((45*A*a^8*b^2)/14 + (5*B*a^9*b)/7) + x^9*((45*B*a^2*b^8
)/7 + (10*A*a*b^9)/7) + x^10*((A*b^10)/6 + (5*B*a*b^9)/3) + x^4*((35*A*a^6*b^4)/2 + 10*B*a^7*b^3) + x^8*((45*A
*a^2*b^8)/8 + 15*B*a^3*b^7) + x^7*((40*A*a^3*b^7)/3 + (70*B*a^4*b^6)/3) + x^6*(21*A*a^4*b^6 + (126*B*a^5*b^5)/
5) + x^3*((120*A*a^7*b^3)/13 + (45*B*a^8*b^2)/13) + x^5*((252*A*a^5*b^5)/11 + (210*B*a^6*b^4)/11) + (B*b^10*x^
11)/5)/x^16

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