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(1)/(x-1)+(1)/(x+5)=(6)/(7)...

(1)/(x-1)+(1)/(x+5)=(6)/(7)

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The value of the integral int_(0)^(1) x(1 - x)^(5)dx is equal to a) (1)/(6) b) (1)/(7) c) (6)/(7) d) (1)/(42)

int(1)/((2x+1)^((5)/(6))(3x+5)^((7)/(6)))dx=

int (1)/((2x+1)^((5)/(6))(3x+5)^((7)/(6)))dx=

(x-1)/(x-2)-(x-2)/(x-3)=(x-5)/(x-6)-(x-6)/(x-7)

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)+…)

Show that int_(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5))

((2)/(3)x+4)((3)/(2)x+6)-((1)/(7)x-1)((1)/(7)x+1)