3.12.85 \(\int \frac {(c+d x)^7}{(a+b x)^9} \, dx\)

Optimal. Leaf size=28 \[ -\frac {(c+d x)^8}{8 (a+b x)^8 (b c-a d)} \]

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Rubi [A]  time = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {37} \begin {gather*} -\frac {(c+d x)^8}{8 (a+b x)^8 (b c-a d)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(c + d*x)^7/(a + b*x)^9,x]

[Out]

-(c + d*x)^8/(8*(b*c - a*d)*(a + b*x)^8)

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]

Rubi steps

\begin {align*} \int \frac {(c+d x)^7}{(a+b x)^9} \, dx &=-\frac {(c+d x)^8}{8 (b c-a d) (a+b x)^8}\\ \end {align*}

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Mathematica [B]  time = 0.13, size = 353, normalized size = 12.61 \begin {gather*} -\frac {a^7 d^7+a^6 b d^6 (c+8 d x)+a^5 b^2 d^5 \left (c^2+8 c d x+28 d^2 x^2\right )+a^4 b^3 d^4 \left (c^3+8 c^2 d x+28 c d^2 x^2+56 d^3 x^3\right )+a^3 b^4 d^3 \left (c^4+8 c^3 d x+28 c^2 d^2 x^2+56 c d^3 x^3+70 d^4 x^4\right )+a^2 b^5 d^2 \left (c^5+8 c^4 d x+28 c^3 d^2 x^2+56 c^2 d^3 x^3+70 c d^4 x^4+56 d^5 x^5\right )+a b^6 d \left (c^6+8 c^5 d x+28 c^4 d^2 x^2+56 c^3 d^3 x^3+70 c^2 d^4 x^4+56 c d^5 x^5+28 d^6 x^6\right )+b^7 \left (c^7+8 c^6 d x+28 c^5 d^2 x^2+56 c^4 d^3 x^3+70 c^3 d^4 x^4+56 c^2 d^5 x^5+28 c d^6 x^6+8 d^7 x^7\right )}{8 b^8 (a+b x)^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(c + d*x)^7/(a + b*x)^9,x]

[Out]

-1/8*(a^7*d^7 + a^6*b*d^6*(c + 8*d*x) + a^5*b^2*d^5*(c^2 + 8*c*d*x + 28*d^2*x^2) + a^4*b^3*d^4*(c^3 + 8*c^2*d*
x + 28*c*d^2*x^2 + 56*d^3*x^3) + a^3*b^4*d^3*(c^4 + 8*c^3*d*x + 28*c^2*d^2*x^2 + 56*c*d^3*x^3 + 70*d^4*x^4) +
a^2*b^5*d^2*(c^5 + 8*c^4*d*x + 28*c^3*d^2*x^2 + 56*c^2*d^3*x^3 + 70*c*d^4*x^4 + 56*d^5*x^5) + a*b^6*d*(c^6 + 8
*c^5*d*x + 28*c^4*d^2*x^2 + 56*c^3*d^3*x^3 + 70*c^2*d^4*x^4 + 56*c*d^5*x^5 + 28*d^6*x^6) + b^7*(c^7 + 8*c^6*d*
x + 28*c^5*d^2*x^2 + 56*c^4*d^3*x^3 + 70*c^3*d^4*x^4 + 56*c^2*d^5*x^5 + 28*c*d^6*x^6 + 8*d^7*x^7))/(b^8*(a + b
*x)^8)

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(c+d x)^7}{(a+b x)^9} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^9,x]

[Out]

IntegrateAlgebraic[(c + d*x)^7/(a + b*x)^9, x]

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fricas [B]  time = 1.39, size = 509, normalized size = 18.18 \begin {gather*} -\frac {8 \, b^{7} d^{7} x^{7} + b^{7} c^{7} + a b^{6} c^{6} d + a^{2} b^{5} c^{5} d^{2} + a^{3} b^{4} c^{4} d^{3} + a^{4} b^{3} c^{3} d^{4} + a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7} + 28 \, {\left (b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 56 \, {\left (b^{7} c^{2} d^{5} + a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 70 \, {\left (b^{7} c^{3} d^{4} + a b^{6} c^{2} d^{5} + a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 56 \, {\left (b^{7} c^{4} d^{3} + a b^{6} c^{3} d^{4} + a^{2} b^{5} c^{2} d^{5} + a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 28 \, {\left (b^{7} c^{5} d^{2} + a b^{6} c^{4} d^{3} + a^{2} b^{5} c^{3} d^{4} + a^{3} b^{4} c^{2} d^{5} + a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 8 \, {\left (b^{7} c^{6} d + a b^{6} c^{5} d^{2} + a^{2} b^{5} c^{4} d^{3} + a^{3} b^{4} c^{3} d^{4} + a^{4} b^{3} c^{2} d^{5} + a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{8 \, {\left (b^{16} x^{8} + 8 \, a b^{15} x^{7} + 28 \, a^{2} b^{14} x^{6} + 56 \, a^{3} b^{13} x^{5} + 70 \, a^{4} b^{12} x^{4} + 56 \, a^{5} b^{11} x^{3} + 28 \, a^{6} b^{10} x^{2} + 8 \, a^{7} b^{9} x + a^{8} b^{8}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^7/(b*x+a)^9,x, algorithm="fricas")

[Out]

-1/8*(8*b^7*d^7*x^7 + b^7*c^7 + a*b^6*c^6*d + a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3 + a^4*b^3*c^3*d^4 + a^5*b^2*c^
2*d^5 + a^6*b*c*d^6 + a^7*d^7 + 28*(b^7*c*d^6 + a*b^6*d^7)*x^6 + 56*(b^7*c^2*d^5 + a*b^6*c*d^6 + a^2*b^5*d^7)*
x^5 + 70*(b^7*c^3*d^4 + a*b^6*c^2*d^5 + a^2*b^5*c*d^6 + a^3*b^4*d^7)*x^4 + 56*(b^7*c^4*d^3 + a*b^6*c^3*d^4 + a
^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + a^4*b^3*d^7)*x^3 + 28*(b^7*c^5*d^2 + a*b^6*c^4*d^3 + a^2*b^5*c^3*d^4 + a^3*b^
4*c^2*d^5 + a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^2 + 8*(b^7*c^6*d + a*b^6*c^5*d^2 + a^2*b^5*c^4*d^3 + a^3*b^4*c^3*d^
4 + a^4*b^3*c^2*d^5 + a^5*b^2*c*d^6 + a^6*b*d^7)*x)/(b^16*x^8 + 8*a*b^15*x^7 + 28*a^2*b^14*x^6 + 56*a^3*b^13*x
^5 + 70*a^4*b^12*x^4 + 56*a^5*b^11*x^3 + 28*a^6*b^10*x^2 + 8*a^7*b^9*x + a^8*b^8)

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giac [B]  time = 1.29, size = 489, normalized size = 17.46 \begin {gather*} -\frac {8 \, b^{7} d^{7} x^{7} + 28 \, b^{7} c d^{6} x^{6} + 28 \, a b^{6} d^{7} x^{6} + 56 \, b^{7} c^{2} d^{5} x^{5} + 56 \, a b^{6} c d^{6} x^{5} + 56 \, a^{2} b^{5} d^{7} x^{5} + 70 \, b^{7} c^{3} d^{4} x^{4} + 70 \, a b^{6} c^{2} d^{5} x^{4} + 70 \, a^{2} b^{5} c d^{6} x^{4} + 70 \, a^{3} b^{4} d^{7} x^{4} + 56 \, b^{7} c^{4} d^{3} x^{3} + 56 \, a b^{6} c^{3} d^{4} x^{3} + 56 \, a^{2} b^{5} c^{2} d^{5} x^{3} + 56 \, a^{3} b^{4} c d^{6} x^{3} + 56 \, a^{4} b^{3} d^{7} x^{3} + 28 \, b^{7} c^{5} d^{2} x^{2} + 28 \, a b^{6} c^{4} d^{3} x^{2} + 28 \, a^{2} b^{5} c^{3} d^{4} x^{2} + 28 \, a^{3} b^{4} c^{2} d^{5} x^{2} + 28 \, a^{4} b^{3} c d^{6} x^{2} + 28 \, a^{5} b^{2} d^{7} x^{2} + 8 \, b^{7} c^{6} d x + 8 \, a b^{6} c^{5} d^{2} x + 8 \, a^{2} b^{5} c^{4} d^{3} x + 8 \, a^{3} b^{4} c^{3} d^{4} x + 8 \, a^{4} b^{3} c^{2} d^{5} x + 8 \, a^{5} b^{2} c d^{6} x + 8 \, a^{6} b d^{7} x + b^{7} c^{7} + a b^{6} c^{6} d + a^{2} b^{5} c^{5} d^{2} + a^{3} b^{4} c^{4} d^{3} + a^{4} b^{3} c^{3} d^{4} + a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7}}{8 \, {\left (b x + a\right )}^{8} b^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^7/(b*x+a)^9,x, algorithm="giac")

[Out]

-1/8*(8*b^7*d^7*x^7 + 28*b^7*c*d^6*x^6 + 28*a*b^6*d^7*x^6 + 56*b^7*c^2*d^5*x^5 + 56*a*b^6*c*d^6*x^5 + 56*a^2*b
^5*d^7*x^5 + 70*b^7*c^3*d^4*x^4 + 70*a*b^6*c^2*d^5*x^4 + 70*a^2*b^5*c*d^6*x^4 + 70*a^3*b^4*d^7*x^4 + 56*b^7*c^
4*d^3*x^3 + 56*a*b^6*c^3*d^4*x^3 + 56*a^2*b^5*c^2*d^5*x^3 + 56*a^3*b^4*c*d^6*x^3 + 56*a^4*b^3*d^7*x^3 + 28*b^7
*c^5*d^2*x^2 + 28*a*b^6*c^4*d^3*x^2 + 28*a^2*b^5*c^3*d^4*x^2 + 28*a^3*b^4*c^2*d^5*x^2 + 28*a^4*b^3*c*d^6*x^2 +
28*a^5*b^2*d^7*x^2 + 8*b^7*c^6*d*x + 8*a*b^6*c^5*d^2*x + 8*a^2*b^5*c^4*d^3*x + 8*a^3*b^4*c^3*d^4*x + 8*a^4*b^
3*c^2*d^5*x + 8*a^5*b^2*c*d^6*x + 8*a^6*b*d^7*x + b^7*c^7 + a*b^6*c^6*d + a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3 +
a^4*b^3*c^3*d^4 + a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + a^7*d^7)/((b*x + a)^8*b^8)

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maple [B]  time = 0.01, size = 464, normalized size = 16.57 \begin {gather*} -\frac {d^{7}}{\left (b x +a \right ) b^{8}}+\frac {7 \left (a d -b c \right ) d^{6}}{2 \left (b x +a \right )^{2} b^{8}}-\frac {7 \left (a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right ) d^{5}}{\left (b x +a \right )^{3} b^{8}}+\frac {35 \left (a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right ) d^{4}}{4 \left (b x +a \right )^{4} b^{8}}-\frac {7 \left (a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right ) d^{3}}{\left (b x +a \right )^{5} b^{8}}+\frac {7 \left (a^{5} d^{5}-5 a^{4} b c \,d^{4}+10 a^{3} b^{2} c^{2} d^{3}-10 a^{2} b^{3} c^{3} d^{2}+5 a \,b^{4} c^{4} d -b^{5} c^{5}\right ) d^{2}}{2 \left (b x +a \right )^{6} b^{8}}-\frac {\left (a^{6} d^{6}-6 a^{5} b c \,d^{5}+15 a^{4} b^{2} c^{2} d^{4}-20 a^{3} b^{3} c^{3} d^{3}+15 a^{2} b^{4} c^{4} d^{2}-6 a \,b^{5} c^{5} d +b^{6} c^{6}\right ) d}{\left (b x +a \right )^{7} b^{8}}-\frac {-a^{7} d^{7}+7 a^{6} b c \,d^{6}-21 a^{5} b^{2} c^{2} d^{5}+35 a^{4} c^{3} d^{4} b^{3}-35 a^{3} b^{4} c^{4} d^{3}+21 a^{2} c^{5} d^{2} b^{5}-7 a \,b^{6} c^{6} d +b^{7} c^{7}}{8 \left (b x +a \right )^{8} b^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^7/(b*x+a)^9,x)

[Out]

-1/8*(-a^7*d^7+7*a^6*b*c*d^6-21*a^5*b^2*c^2*d^5+35*a^4*b^3*c^3*d^4-35*a^3*b^4*c^4*d^3+21*a^2*b^5*c^5*d^2-7*a*b
^6*c^6*d+b^7*c^7)/b^8/(b*x+a)^8-7*d^5*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^8/(b*x+a)^3-d*(a^6*d^6-6*a^5*b*c*d^5+15*a^
4*b^2*c^2*d^4-20*a^3*b^3*c^3*d^3+15*a^2*b^4*c^4*d^2-6*a*b^5*c^5*d+b^6*c^6)/b^8/(b*x+a)^7-7*d^3*(a^4*d^4-4*a^3*
b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/b^8/(b*x+a)^5+7/2*d^6*(a*d-b*c)/b^8/(b*x+a)^2+35/4*d^4*(a^3*d
^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/b^8/(b*x+a)^4-d^7/b^8/(b*x+a)+7/2*d^2*(a^5*d^5-5*a^4*b*c*d^4+10*a^3*b^
2*c^2*d^3-10*a^2*b^3*c^3*d^2+5*a*b^4*c^4*d-b^5*c^5)/b^8/(b*x+a)^6

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maxima [B]  time = 1.65, size = 509, normalized size = 18.18 \begin {gather*} -\frac {8 \, b^{7} d^{7} x^{7} + b^{7} c^{7} + a b^{6} c^{6} d + a^{2} b^{5} c^{5} d^{2} + a^{3} b^{4} c^{4} d^{3} + a^{4} b^{3} c^{3} d^{4} + a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7} + 28 \, {\left (b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 56 \, {\left (b^{7} c^{2} d^{5} + a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 70 \, {\left (b^{7} c^{3} d^{4} + a b^{6} c^{2} d^{5} + a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 56 \, {\left (b^{7} c^{4} d^{3} + a b^{6} c^{3} d^{4} + a^{2} b^{5} c^{2} d^{5} + a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 28 \, {\left (b^{7} c^{5} d^{2} + a b^{6} c^{4} d^{3} + a^{2} b^{5} c^{3} d^{4} + a^{3} b^{4} c^{2} d^{5} + a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 8 \, {\left (b^{7} c^{6} d + a b^{6} c^{5} d^{2} + a^{2} b^{5} c^{4} d^{3} + a^{3} b^{4} c^{3} d^{4} + a^{4} b^{3} c^{2} d^{5} + a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{8 \, {\left (b^{16} x^{8} + 8 \, a b^{15} x^{7} + 28 \, a^{2} b^{14} x^{6} + 56 \, a^{3} b^{13} x^{5} + 70 \, a^{4} b^{12} x^{4} + 56 \, a^{5} b^{11} x^{3} + 28 \, a^{6} b^{10} x^{2} + 8 \, a^{7} b^{9} x + a^{8} b^{8}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^7/(b*x+a)^9,x, algorithm="maxima")

[Out]

-1/8*(8*b^7*d^7*x^7 + b^7*c^7 + a*b^6*c^6*d + a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3 + a^4*b^3*c^3*d^4 + a^5*b^2*c^
2*d^5 + a^6*b*c*d^6 + a^7*d^7 + 28*(b^7*c*d^6 + a*b^6*d^7)*x^6 + 56*(b^7*c^2*d^5 + a*b^6*c*d^6 + a^2*b^5*d^7)*
x^5 + 70*(b^7*c^3*d^4 + a*b^6*c^2*d^5 + a^2*b^5*c*d^6 + a^3*b^4*d^7)*x^4 + 56*(b^7*c^4*d^3 + a*b^6*c^3*d^4 + a
^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + a^4*b^3*d^7)*x^3 + 28*(b^7*c^5*d^2 + a*b^6*c^4*d^3 + a^2*b^5*c^3*d^4 + a^3*b^
4*c^2*d^5 + a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^2 + 8*(b^7*c^6*d + a*b^6*c^5*d^2 + a^2*b^5*c^4*d^3 + a^3*b^4*c^3*d^
4 + a^4*b^3*c^2*d^5 + a^5*b^2*c*d^6 + a^6*b*d^7)*x)/(b^16*x^8 + 8*a*b^15*x^7 + 28*a^2*b^14*x^6 + 56*a^3*b^13*x
^5 + 70*a^4*b^12*x^4 + 56*a^5*b^11*x^3 + 28*a^6*b^10*x^2 + 8*a^7*b^9*x + a^8*b^8)

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mupad [B]  time = 0.17, size = 571, normalized size = 20.39 \begin {gather*} -\frac {a^7\,d^7+a^6\,b\,c\,d^6+8\,a^6\,b\,d^7\,x+a^5\,b^2\,c^2\,d^5+8\,a^5\,b^2\,c\,d^6\,x+28\,a^5\,b^2\,d^7\,x^2+a^4\,b^3\,c^3\,d^4+8\,a^4\,b^3\,c^2\,d^5\,x+28\,a^4\,b^3\,c\,d^6\,x^2+56\,a^4\,b^3\,d^7\,x^3+a^3\,b^4\,c^4\,d^3+8\,a^3\,b^4\,c^3\,d^4\,x+28\,a^3\,b^4\,c^2\,d^5\,x^2+56\,a^3\,b^4\,c\,d^6\,x^3+70\,a^3\,b^4\,d^7\,x^4+a^2\,b^5\,c^5\,d^2+8\,a^2\,b^5\,c^4\,d^3\,x+28\,a^2\,b^5\,c^3\,d^4\,x^2+56\,a^2\,b^5\,c^2\,d^5\,x^3+70\,a^2\,b^5\,c\,d^6\,x^4+56\,a^2\,b^5\,d^7\,x^5+a\,b^6\,c^6\,d+8\,a\,b^6\,c^5\,d^2\,x+28\,a\,b^6\,c^4\,d^3\,x^2+56\,a\,b^6\,c^3\,d^4\,x^3+70\,a\,b^6\,c^2\,d^5\,x^4+56\,a\,b^6\,c\,d^6\,x^5+28\,a\,b^6\,d^7\,x^6+b^7\,c^7+8\,b^7\,c^6\,d\,x+28\,b^7\,c^5\,d^2\,x^2+56\,b^7\,c^4\,d^3\,x^3+70\,b^7\,c^3\,d^4\,x^4+56\,b^7\,c^2\,d^5\,x^5+28\,b^7\,c\,d^6\,x^6+8\,b^7\,d^7\,x^7}{8\,a^8\,b^8+64\,a^7\,b^9\,x+224\,a^6\,b^{10}\,x^2+448\,a^5\,b^{11}\,x^3+560\,a^4\,b^{12}\,x^4+448\,a^3\,b^{13}\,x^5+224\,a^2\,b^{14}\,x^6+64\,a\,b^{15}\,x^7+8\,b^{16}\,x^8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^7/(a + b*x)^9,x)

[Out]

-(a^7*d^7 + b^7*c^7 + 8*b^7*d^7*x^7 + 28*a*b^6*d^7*x^6 + 28*b^7*c*d^6*x^6 + a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3
+ a^4*b^3*c^3*d^4 + a^5*b^2*c^2*d^5 + 28*a^5*b^2*d^7*x^2 + 56*a^4*b^3*d^7*x^3 + 70*a^3*b^4*d^7*x^4 + 56*a^2*b^
5*d^7*x^5 + 28*b^7*c^5*d^2*x^2 + 56*b^7*c^4*d^3*x^3 + 70*b^7*c^3*d^4*x^4 + 56*b^7*c^2*d^5*x^5 + a*b^6*c^6*d +
a^6*b*c*d^6 + 8*a^6*b*d^7*x + 8*b^7*c^6*d*x + 28*a^2*b^5*c^3*d^4*x^2 + 28*a^3*b^4*c^2*d^5*x^2 + 56*a^2*b^5*c^2
*d^5*x^3 + 8*a*b^6*c^5*d^2*x + 8*a^5*b^2*c*d^6*x + 56*a*b^6*c*d^6*x^5 + 8*a^2*b^5*c^4*d^3*x + 8*a^3*b^4*c^3*d^
4*x + 8*a^4*b^3*c^2*d^5*x + 28*a*b^6*c^4*d^3*x^2 + 28*a^4*b^3*c*d^6*x^2 + 56*a*b^6*c^3*d^4*x^3 + 56*a^3*b^4*c*
d^6*x^3 + 70*a*b^6*c^2*d^5*x^4 + 70*a^2*b^5*c*d^6*x^4)/(8*a^8*b^8 + 8*b^16*x^8 + 64*a^7*b^9*x + 64*a*b^15*x^7
+ 224*a^6*b^10*x^2 + 448*a^5*b^11*x^3 + 560*a^4*b^12*x^4 + 448*a^3*b^13*x^5 + 224*a^2*b^14*x^6)

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sympy [F(-1)]  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((d*x+c)**7/(b*x+a)**9,x)

[Out]

Timed out

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