[x+x log x],[" 8."x sqrt(1+2x^(2))]

If y = x log |x + sqrt(1 + x ^(2)) |- sqrt(1 + x ^(2)) then (dy )/(dx )=

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))

f(x)=2x+cot^(-1)x-log|x + sqrt(1+x^(2))| is …………..

The value of int_(-1)^(1) ((logx+sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(x) dx-int_(-1)^(1) (log(x sqrt(1+x^(2))))/(x+log(x+logsqrt(1+x^(2))))f(-x)dx ,

If f(x)=2x+cos^(-1) x+log (sqrt(1+x^(2))-x) , then f(x) is-

Find the integral int(1)/(sqrt((1-x)(2-x)))dx A. log(2x-3)+sqrt((2x-3)^(2)-1)+Cquad B. log(2x-3)-sqrt((2x-3)^(2)+1)+C C. log(2x+3)-sqrt((2x+3)^(2)-1)+Cquad D. log(2x+3)+sqrt((2x+3)^(2)+1)+C

Choose the correct answer int sqrt(1+x^2) d x is equal to A) x/2 sqrt(1+x^2)+1/2 log |x+sqrt(1+x^2)|+C B) 2/3(1+x^2)^(3 / 2)+C C) 3/2 x(1+x^2)^(3 / 2)+C D) x^2/2 sqrt(1+x^2)+1/2 x^2 log |x+sqrt(1+x^2)|+C