" 33."(x sqrt(1+x))/((1+x^(2))^(3/2))

int(x^(3))/(sqrt(1+x^(2)))dx=a(1+x^(2))^((3)/(2))+b* sqrt(1+x^(2))+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

The value of integral inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi se q u a lto e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c none of these

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

underset(x to 0)"Lt" (sqrt(1+x^(2))-sqrt(1-x+x^(2)))/(3^(x)-1)=

int((1)/(sqrt(x))+(2)/(sqrt(x^(2)-1))-(3)/(2x^(2)))dx on (1,oo)

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=