(4.)int(sum(r=0)^(oo)(x^(r)3^(r))/(r!))d...

(4.)int(sum_(r=0)^(oo)(x^(r)3^(r))/(r!))dx=

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int (sum_(r = 0)^(infty) (x^(r) 3^(r))/(r!) ) dx =

int(sum_(r=0)^(oo)(x^(r)backslash2^(r))/(r!))dx=(A)e^(x)+C(B)(e^(2x))/(2)+C(C)-(2)/(1-2x)+C(D)2e^(2x)+C

sum_(r=1)^(oo)((4r+5)5^(-r))/(r(5r+5))

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sum_(r=0)^(oo)((r+1)((2)/(3))^(r)) is

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