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" 3."2^(x)+(5)/(x)-(1)/(x^(1/3))...

" 3."2^(x)+(5)/(x)-(1)/(x^(1/3))

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(5x)/(3)-(x-2)/(3)=(9)/(4)-(1)/(2)(x-(2x-1)/(3))

int(x+(1)/(x))^(3/2)((x^(2)-1)/(x^(2)))dx is equal to (A) (1)/(3)(x+(1)/(x))^(3)+C (B)(2)/(5)(x+(1)/(x))^(5/2)

Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)/(2)log((3)/(2)) Reason (R ) : If |x| lt 1 then log_(e )((1+x)/(1-x))=2(x+(x^(3))/(3)+(x^(5))/(5)+…)

If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x^(5)) +…=

If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x^(5)) +…=

Add :5x^(2)-(1)/(3)x+(5)/(2),-(1)/(2)x^(2)+(1)/(2)x-(1)/(3) and -2x^(2)+(1)/(5)x-(1)/(6)

(3)/(x+1)-(2)/(x-1)=(5)/(x^(2)-1)

(1)/(2x+1)+(1)/(3)(1)/((2x+1)^(3))+(1)/(5)(1)/((2x+1)^(5))+....=

(1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=