`x^((x-1)- 1/2 (x-1)^2+1/3((x-1)^3).- 1/4((x-1)^4).+……..` is equal to (A) `2logx` (B) `logx` (C) `x^2` (D) none of these

int[1/logx-1/(logx)^2]dx= (A) x/logx (B) xlogx (C) logx/x (D) none of these

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), (x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

The value of the integral int(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))dx is equal to (A) x^2+c (B) x^3/3+c (C) x^2/2+c (D) none of these

tan((pi)/(4)+(1)/(2)cos^(-1)x)+tan((pi)/(4)-(1)/(2)cos^(-1)x),x!=0 is equal to x( b) 2x( c) (2)/(x) (d) none of these

inte^(x)((x-1)(x-logx))/(x^(2))dx is equal to

Value of ((x-1)^(3)+(2x-1)^(3)-(3x2)^(3))/((x-1)(2x-1)(3x-2)) is equal to (A)-3(B)0(C)1(D)3

intlogx/(1+logx)^2dx= (A) 1/(1+logx)+c (B) x/(1+logx)+c (C) loglog(1+logx)+c (D) none of these

∫ (1)/(x.logx.(2+logx))

The value of (1-x^4)/(1+x)+(1+x^2)/xxx1/(x(1-x)) is (a) 1 (b) 1-x^2 (c) 1/x (d) 1+x (e) None of these

int(log_e(x+1)-log_ex)/(x(x+1))dx is equal to (A) -1/2[log(x+1)^2-1/2logx]^2+log_e(x+1)log_ex+C (B) -[(log_e(x+1)-log_ex]^2 (C) c-1/2(log(1+1/x))^2 (D) none of these