3.2 Test file Number [57]

3.2.1 Mathematica

Integral number [166] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{d+ex}dx$$

[B]   time = 0.067911 (sec), size = 72 ,normalized size = 2.77 $$\frac{x(fx{)}^m(-bn{}_3{F}_2(1,1+m,1+m;2+m,2+m;-\frac{ex}{d})+(1+m){}_2{F}_1(1,1+m;2+m;-\frac{ex}{d})(a+b\log \left(c{x}^n\right)))}{d(1+m{)}^2}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x),x]

[Out]

(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, 1 + m, 1 + m}, {2 + m, 2 + m}, -((e*x)/d)]) + (1 + m)*Hypergeometric2F
1[1, 1 + m, 2 + m, -((e*x)/d)]*(a + b*Log[c*x^n])))/(d*(1 + m)^2)

Integral number [167] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{(d+ex{)}^2}dx$$

[B]   time = 0.064168 (sec), size = 72 ,normalized size = 2.77 $$\frac{x(fx{)}^m(-bn{}_3{F}_2(2,1+m,1+m;2+m,2+m;-\frac{ex}{d})+(1+m){}_2{F}_1(2,1+m;2+m;-\frac{ex}{d})(a+b\log \left(c{x}^n\right)))}{d^2(1+m{)}^2}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x)^2,x]

[Out]

(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{2, 1 + m, 1 + m}, {2 + m, 2 + m}, -((e*x)/d)]) + (1 + m)*Hypergeometric2F
1[2, 1 + m, 2 + m, -((e*x)/d)]*(a + b*Log[c*x^n])))/(d^2*(1 + m)^2)

Integral number [168] $$\int x(a+bx{)}^m\log \left(c{x}^n\right)dx$$

[B]   time = 0.171397 (sec), size = 173 ,normalized size = 9.61 $$\frac{(a+bx{)}^m{(1+\frac{bx}{a})}^{-m}(-n(2abx{(1+\frac{bx}{a})}^m+b^2{x}^2{(1+\frac{bx}{a})}^m+a^2(-1+{(1+\frac{bx}{a})}^m))+ab(2+m)nx{}_3{F}_2(1,1,-1-m;2,2;-\frac{bx}{a})+(abmx{(1+\frac{bx}{a})}^m+b^2(1+m)x^2{(1+\frac{bx}{a})}^m-a^2(-1+{(1+\frac{bx}{a})}^m))\log \left(c{x}^n\right))}{b^2(1+m)(2+m)}$$

[In]

Integrate[x*(a + b*x)^m*Log[c*x^n],x]

[Out]

((a + b*x)^m*(-(n*(2*a*b*x*(1 + (b*x)/a)^m + b^2*x^2*(1 + (b*x)/a)^m + a^2*(-1 + (1 + (b*x)/a)^m))) + a*b*(2 +
m)*n*x*HypergeometricPFQ[{1, 1, -1 - m}, {2, 2}, -((b*x)/a)] + (a*b*m*x*(1 + (b*x)/a)^m + b^2*(1 + m)*x^2*(1
+ (b*x)/a)^m - a^2*(-1 + (1 + (b*x)/a)^m))*Log[c*x^n]))/(b^2*(1 + m)*(2 + m)*(1 + (b*x)/a)^m)

Integral number [170] $$\int \frac{(a+bx{)}^m\log \left(c{x}^n\right)}{x}dx$$

[B]   time = 0.043397 (sec), size = 89 ,normalized size = 4.45 $$\frac{{(1+\frac{a}{bx})}^{-m}(a+bx{)}^m(-n{}_3{F}_2(-m,-m,-m;1-m,1-m;-\frac{a}{bx})+m{}_2{F}_1(-m,-m;1-m;-\frac{a}{bx})\log \left(c{x}^n\right))}{m^2}$$

[In]

Integrate[((a + b*x)^m*Log[c*x^n])/x,x]

[Out]

((a + b*x)^m*(-(n*HypergeometricPFQ[{-m, -m, -m}, {1 - m, 1 - m}, -(a/(b*x))]) + m*Hypergeometric2F1[-m, -m, 1
- m, -(a/(b*x))]*Log[c*x^n]))/(m^2*(1 + a/(b*x))^m)

Integral number [322] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{d+e{x}^2}dx$$

[B]   time = 0.148536 (sec), size = 108 ,normalized size = 3.86 $$\frac{x(fx{)}^m(-bn{}_3{F}_2(1,\frac{1}{2}+\frac{m}{2},\frac{1}{2}+\frac{m}{2};\frac{3}{2}+\frac{m}{2},\frac{3}{2}+\frac{m}{2};-\frac{e{x}^2}{d})+(1+m){}_2{F}_1(1,\frac{1+m}{2};\frac{3+m}{2};-\frac{e{x}^2}{d})(a+b\log \left(c{x}^n\right)))}{d(1+m{)}^2}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2),x]

[Out]

(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, 1/2 + m/2, 1/2 + m/2}, {3/2 + m/2, 3/2 + m/2}, -((e*x^2)/d)]) + (1 + m
)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)]*(a + b*Log[c*x^n])))/(d*(1 + m)^2)

Integral number [323] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{{(d+e{x}^2)}^2}dx$$

[B]   time = 0.073768 (sec), size = 108 ,normalized size = 3.86 $$\frac{x(fx{)}^m(-bn{}_3{F}_2(2,\frac{1}{2}+\frac{m}{2},\frac{1}{2}+\frac{m}{2};\frac{3}{2}+\frac{m}{2},\frac{3}{2}+\frac{m}{2};-\frac{e{x}^2}{d})+(1+m){}_2{F}_1(2,\frac{1+m}{2};\frac{3+m}{2};-\frac{e{x}^2}{d})(a+b\log \left(c{x}^n\right)))}{d^2(1+m{)}^2}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^2)^2,x]

[Out]

(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{2, 1/2 + m/2, 1/2 + m/2}, {3/2 + m/2, 3/2 + m/2}, -((e*x^2)/d)]) + (1 + m
)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((e*x^2)/d)]*(a + b*Log[c*x^n])))/(d^2*(1 + m)^2)

Integral number [406] $$\int \frac{x^3(a+b\log \left(c{x}^n\right))}{d+e{x}^r}dx$$

[B]   time = 0.071534 (sec), size = 87 ,normalized size = 3.35 $$\frac{x^4(-bn{}_3{F}_2(1,\frac{4}{r},\frac{4}{r};1+\frac{4}{r},1+\frac{4}{r};-\frac{e{x}^r}{d})+4{}_2{F}_1(1,\frac{4}{r};\frac{4+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right)))}{16d}$$

[In]

Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r),x]

[Out]

(x^4*(-(b*n*HypergeometricPFQ[{1, 4/r, 4/r}, {1 + 4/r, 1 + 4/r}, -((e*x^r)/d)]) + 4*Hypergeometric2F1[1, 4/r,
(4 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(16*d)

Integral number [407] $$\int \frac{x(a+b\log \left(c{x}^n\right))}{d+e{x}^r}dx$$

[B]   time = 0.065757 (sec), size = 87 ,normalized size = 3.62 $$\frac{x^2(-bn{}_3{F}_2(1,\frac{2}{r},\frac{2}{r};1+\frac{2}{r},1+\frac{2}{r};-\frac{e{x}^r}{d})+2{}_2{F}_1(1,\frac{2}{r};\frac{2+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right)))}{4d}$$

[In]

Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^r),x]

[Out]

(x^2*(-(b*n*HypergeometricPFQ[{1, 2/r, 2/r}, {1 + 2/r, 1 + 2/r}, -((e*x^r)/d)]) + 2*Hypergeometric2F1[1, 2/r,
(2 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(4*d)

Integral number [409] $$\int \frac{a+b\log \left(c{x}^n\right)}{x^3(d+e{x}^r)}dx$$

[B]   time = 0.065247 (sec), size = 86 ,normalized size = 3.31 $$-\frac{bn{}_3{F}_2(1,-\frac{2}{r},-\frac{2}{r};1-\frac{2}{r},1-\frac{2}{r};-\frac{e{x}^r}{d})+2{}_2{F}_1(1,-\frac{2}{r};\frac{-2+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right))}{4d{x}^2}$$

[In]

Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)),x]

[Out]

-1/4*(b*n*HypergeometricPFQ[{1, -2/r, -2/r}, {1 - 2/r, 1 - 2/r}, -((e*x^r)/d)] + 2*Hypergeometric2F1[1, -2/r,
(-2 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n]))/(d*x^2)

Integral number [410] $$\int \frac{x^2(a+b\log \left(c{x}^n\right))}{d+e{x}^r}dx$$

[B]   time = 0.066602 (sec), size = 87 ,normalized size = 3.35 $$\frac{x^3(-bn{}_3{F}_2(1,\frac{3}{r},\frac{3}{r};1+\frac{3}{r},1+\frac{3}{r};-\frac{e{x}^r}{d})+3{}_2{F}_1(1,\frac{3}{r};\frac{3+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right)))}{9d}$$

[In]

Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r),x]

[Out]

(x^3*(-(b*n*HypergeometricPFQ[{1, 3/r, 3/r}, {1 + 3/r, 1 + 3/r}, -((e*x^r)/d)]) + 3*Hypergeometric2F1[1, 3/r,
(3 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(9*d)

Integral number [411] $$\int \frac{a+b\log \left(c{x}^n\right)}{d+e{x}^r}dx$$

[B]   time = 0.05181 (sec), size = 69 ,normalized size = 3. $$\frac{x(-bn{}_3{F}_2(1,\frac{1}{r},\frac{1}{r};1+\frac{1}{r},1+\frac{1}{r};-\frac{e{x}^r}{d})+{}_2{F}_1(1,\frac{1}{r};1+\frac{1}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right)))}{d}$$

[In]

Integrate[(a + b*Log[c*x^n])/(d + e*x^r),x]

[Out]

(x*(-(b*n*HypergeometricPFQ[{1, r^(-1), r^(-1)}, {1 + r^(-1), 1 + r^(-1)}, -((e*x^r)/d)]) + Hypergeometric2F1[
1, r^(-1), 1 + r^(-1), -((e*x^r)/d)]*(a + b*Log[c*x^n])))/d

Integral number [412] $$\int \frac{a+b\log \left(c{x}^n\right)}{x^2(d+e{x}^r)}dx$$

[B]   time = 0.064875 (sec), size = 83 ,normalized size = 3.19 $$-\frac{bn{}_3{F}_2(1,-\frac{1}{r},-\frac{1}{r};1-\frac{1}{r},1-\frac{1}{r};-\frac{e{x}^r}{d})+{}_2{F}_1(1,-\frac{1}{r};\frac{-1+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right))}{dx}$$

[In]

Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)),x]

[Out]

-((b*n*HypergeometricPFQ[{1, -r^(-1), -r^(-1)}, {1 - r^(-1), 1 - r^(-1)}, -((e*x^r)/d)] + Hypergeometric2F1[1,
-r^(-1), (-1 + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n]))/(d*x))

Integral number [413] $$\int \frac{x^3(a+b\log \left(c{x}^n\right))}{{(d+e{x}^r)}^2}dx$$

[B]   time = 0.161798 (sec), size = 140 ,normalized size = 5.38 $$\frac{x^4(-bn(-4+r)(d+e{x}^r){}_3{F}_2(1,\frac{4}{r},\frac{4}{r};1+\frac{4}{r},1+\frac{4}{r};-\frac{e{x}^r}{d})+16d(a+b\log \left(c{x}^n\right))+4(d+e{x}^r){}_2{F}_1(1,\frac{4}{r};\frac{4+r}{r};-\frac{e{x}^r}{d})(-bn+a(-4+r)+b(-4+r)\log \left(c{x}^n\right)))}{16d^{2}r(d+e{x}^r)}$$

[In]

Integrate[(x^3*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]

[Out]

(x^4*(-(b*n*(-4 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 4/r, 4/r}, {1 + 4/r, 1 + 4/r}, -((e*x^r)/d)]) + 16*d*(a
+ b*Log[c*x^n]) + 4*(d + e*x^r)*Hypergeometric2F1[1, 4/r, (4 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-4 + r) + b*(
-4 + r)*Log[c*x^n])))/(16*d^2*r*(d + e*x^r))

Integral number [414] $$\int \frac{x(a+b\log \left(c{x}^n\right))}{{(d+e{x}^r)}^2}dx$$

[B]   time = 0.149491 (sec), size = 140 ,normalized size = 5.83 $$\frac{x^2(-bn(-2+r)(d+e{x}^r){}_3{F}_2(1,\frac{2}{r},\frac{2}{r};1+\frac{2}{r},1+\frac{2}{r};-\frac{e{x}^r}{d})+4d(a+b\log \left(c{x}^n\right))+2(d+e{x}^r){}_2{F}_1(1,\frac{2}{r};\frac{2+r}{r};-\frac{e{x}^r}{d})(-bn+a(-2+r)+b(-2+r)\log \left(c{x}^n\right)))}{4d^{2}r(d+e{x}^r)}$$

[In]

Integrate[(x*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]

[Out]

(x^2*(-(b*n*(-2 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 2/r, 2/r}, {1 + 2/r, 1 + 2/r}, -((e*x^r)/d)]) + 4*d*(a
+ b*Log[c*x^n]) + 2*(d + e*x^r)*Hypergeometric2F1[1, 2/r, (2 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-2 + r) + b*(-
2 + r)*Log[c*x^n])))/(4*d^2*r*(d + e*x^r))

Integral number [416] $$\int \frac{a+b\log \left(c{x}^n\right)}{x^3{(d+e{x}^r)}^2}dx$$

[B]   time = 0.150218 (sec), size = 139 ,normalized size = 5.35 $$-\frac{bn(2+r)(d+e{x}^r){}_3{F}_2(1,-\frac{2}{r},-\frac{2}{r};1-\frac{2}{r},1-\frac{2}{r};-\frac{e{x}^r}{d})-4d(a+b\log \left(c{x}^n\right))+2(d+e{x}^r){}_2{F}_1(1,-\frac{2}{r};\frac{-2+r}{r};-\frac{e{x}^r}{d})(-bn+a(2+r)+b(2+r)\log \left(c{x}^n\right))}{4d^{2}r{x}^2(d+e{x}^r)}$$

[In]

Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*x^r)^2),x]

[Out]

-1/4*(b*n*(2 + r)*(d + e*x^r)*HypergeometricPFQ[{1, -2/r, -2/r}, {1 - 2/r, 1 - 2/r}, -((e*x^r)/d)] - 4*d*(a +
b*Log[c*x^n]) + 2*(d + e*x^r)*Hypergeometric2F1[1, -2/r, (-2 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(2 + r) + b*(2
+ r)*Log[c*x^n]))/(d^2*r*x^2*(d + e*x^r))

Integral number [417] $$\int \frac{x^2(a+b\log \left(c{x}^n\right))}{{(d+e{x}^r)}^2}dx$$

[B]   time = 0.152317 (sec), size = 140 ,normalized size = 5.38 $$\frac{x^3(-bn(-3+r)(d+e{x}^r){}_3{F}_2(1,\frac{3}{r},\frac{3}{r};1+\frac{3}{r},1+\frac{3}{r};-\frac{e{x}^r}{d})+9d(a+b\log \left(c{x}^n\right))+3(d+e{x}^r){}_2{F}_1(1,\frac{3}{r};\frac{3+r}{r};-\frac{e{x}^r}{d})(-bn+a(-3+r)+b(-3+r)\log \left(c{x}^n\right)))}{9d^{2}r(d+e{x}^r)}$$

[In]

Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]

[Out]

(x^3*(-(b*n*(-3 + r)*(d + e*x^r)*HypergeometricPFQ[{1, 3/r, 3/r}, {1 + 3/r, 1 + 3/r}, -((e*x^r)/d)]) + 9*d*(a
+ b*Log[c*x^n]) + 3*(d + e*x^r)*Hypergeometric2F1[1, 3/r, (3 + r)/r, -((e*x^r)/d)]*(-(b*n) + a*(-3 + r) + b*(-
3 + r)*Log[c*x^n])))/(9*d^2*r*(d + e*x^r))

Integral number [418] $$\int \frac{a+b\log \left(c{x}^n\right)}{{(d+e{x}^r)}^2}dx$$

[B]   time = 1.97465 (sec), size = 161 ,normalized size = 7. $$\frac{x(adr{}_2{F}_1(2,\frac{1}{r};1+\frac{1}{r};-\frac{e{x}^r}{d})+aer{x}^r{}_2{F}_1(2,\frac{1}{r};1+\frac{1}{r};-\frac{e{x}^r}{d})-bn(-1+r)(d+e{x}^r){}_3{F}_2(1,\frac{1}{r},\frac{1}{r};1+\frac{1}{r},1+\frac{1}{r};-\frac{e{x}^r}{d})+bd\log \left(c{x}^n\right)-b(d+e{x}^r){}_2{F}_1(1,\frac{1}{r};1+\frac{1}{r};-\frac{e{x}^r}{d})(n-(-1+r)\log \left(c{x}^n\right)))}{d^{2}r(d+e{x}^r)}$$

[In]

Integrate[(a + b*Log[c*x^n])/(d + e*x^r)^2,x]

[Out]

(x*(a*d*r*Hypergeometric2F1[2, r^(-1), 1 + r^(-1), -((e*x^r)/d)] + a*e*r*x^r*Hypergeometric2F1[2, r^(-1), 1 +
r^(-1), -((e*x^r)/d)] - b*n*(-1 + r)*(d + e*x^r)*HypergeometricPFQ[{1, r^(-1), r^(-1)}, {1 + r^(-1), 1 + r^(-1
)}, -((e*x^r)/d)] + b*d*Log[c*x^n] - b*(d + e*x^r)*Hypergeometric2F1[1, r^(-1), 1 + r^(-1), -((e*x^r)/d)]*(n -
(-1 + r)*Log[c*x^n])))/(d^2*r*(d + e*x^r))

Integral number [419] $$\int \frac{a+b\log \left(c{x}^n\right)}{x^2{(d+e{x}^r)}^2}dx$$

[B]   time = 0.129567 (sec), size = 135 ,normalized size = 5.19 $$\frac{-bn(1+r)(d+e{x}^r){}_3{F}_2(1,-\frac{1}{r},-\frac{1}{r};1-\frac{1}{r},1-\frac{1}{r};-\frac{e{x}^r}{d})+d(a+b\log \left(c{x}^n\right))-(d+e{x}^r){}_2{F}_1(1,-\frac{1}{r};\frac{-1+r}{r};-\frac{e{x}^r}{d})(a-bn+ar+b(1+r)\log \left(c{x}^n\right))}{d^{2}rx(d+e{x}^r)}$$

[In]

Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*x^r)^2),x]

[Out]

(-(b*n*(1 + r)*(d + e*x^r)*HypergeometricPFQ[{1, -r^(-1), -r^(-1)}, {1 - r^(-1), 1 - r^(-1)}, -((e*x^r)/d)]) +
d*(a + b*Log[c*x^n]) - (d + e*x^r)*Hypergeometric2F1[1, -r^(-1), (-1 + r)/r, -((e*x^r)/d)]*(a - b*n + a*r + b
*(1 + r)*Log[c*x^n]))/(d^2*r*x*(d + e*x^r))

Integral number [444] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{d+e{x}^r}dx$$

[B]   time = 0.089494 (sec), size = 111 ,normalized size = 3.96 $$\frac{x(fx{)}^m(-bn{}_3{F}_2(1,\frac{1}{r}+\frac{m}{r},\frac{1}{r}+\frac{m}{r};1+\frac{1}{r}+\frac{m}{r},1+\frac{1}{r}+\frac{m}{r};-\frac{e{x}^r}{d})+(1+m){}_2{F}_1(1,\frac{1+m}{r};\frac{1+m+r}{r};-\frac{e{x}^r}{d})(a+b\log \left(c{x}^n\right)))}{d(1+m{)}^2}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r),x]

[Out]

(x*(f*x)^m*(-(b*n*HypergeometricPFQ[{1, r^(-1) + m/r, r^(-1) + m/r}, {1 + r^(-1) + m/r, 1 + r^(-1) + m/r}, -((
e*x^r)/d)]) + (1 + m)*Hypergeometric2F1[1, (1 + m)/r, (1 + m + r)/r, -((e*x^r)/d)]*(a + b*Log[c*x^n])))/(d*(1
+ m)^2)

Integral number [445] $$\int \frac{(fx{)}^m(a+b\log \left(c{x}^n\right))}{{(d+e{x}^r)}^2}dx$$

[B]   time = 0.245739 (sec), size = 177 ,normalized size = 6.32 $$\frac{x(fx{)}^m(bn(1+m-r)(d+e{x}^r){}_3{F}_2(1,\frac{1}{r}+\frac{m}{r},\frac{1}{r}+\frac{m}{r};1+\frac{1}{r}+\frac{m}{r},1+\frac{1}{r}+\frac{m}{r};-\frac{e{x}^r}{d})-(1+m)(-d(1+m)(a+b\log \left(c{x}^n\right))+(d+e{x}^r){}_2{F}_1(1,\frac{1+m}{r};\frac{1+m+r}{r};-\frac{e{x}^r}{d})(bn+a(1+m-r)+b(1+m-r)\log \left(c{x}^n\right))))}{d^2(1+m{)}^{2}r(d+e{x}^r)}$$

[In]

Integrate[((f*x)^m*(a + b*Log[c*x^n]))/(d + e*x^r)^2,x]

[Out]

(x*(f*x)^m*(b*n*(1 + m - r)*(d + e*x^r)*HypergeometricPFQ[{1, r^(-1) + m/r, r^(-1) + m/r}, {1 + r^(-1) + m/r,
1 + r^(-1) + m/r}, -((e*x^r)/d)] - (1 + m)*(-(d*(1 + m)*(a + b*Log[c*x^n])) + (d + e*x^r)*Hypergeometric2F1[1,
(1 + m)/r, (1 + m + r)/r, -((e*x^r)/d)]*(b*n + a*(1 + m - r) + b*(1 + m - r)*Log[c*x^n]))))/(d^2*(1 + m)^2*r*
(d + e*x^r))