`intxlogx(logx-1)dx=` (A) `x^2/2(logx-1)^2dx=` (B) `(xlogx)^2+c` (C) `1/2(xlogx+1)^2+c` (D) `2(xlogx-x)^2+c`

int(logx/(1+logx)^2)dx

(1) int x*(logx)^(2)dx

int_1^3 xlogx dx

If int[(logx-1)/(1+(logx)^2)]^2dx=f(x)/(1+(g(x))^2)+c , then (A) f(x)=x (B) f(x)=x^2 (C) g(x)=logx (D) g(x)=(logx)^2

intcos(logx)dx is equal to (A) x/2(cos(logx)-sin(logx))+c (B) x(cos(logx)+sin(logx))+c (C) x/2(cos(logx)+sin(logx)+c (D) x(cos(logx)-sin(logx))+c

int(x dx)/((x-1)(x-2) equal(A) log|((x-1)^2)/(x-2)|+C (B) log|((x-2)^2)/(x-1)|+C (C) log|((x-1)^2)/(x-2)|+C (D) log|(x-1)(x-2)|+C

int((x+1)(x+logx)^2)/(2x)dx

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

int(xcosxlogx-sinx)/(x(logx)^2)dx is equal to (A) sinx+c (B) logxsinx+c (C) logx+sinx+c (D) none of these

Evaluate: (i) intx^x(1+logx)\ dx (ii) intx^(2x)\ (1+logx)\ dx