16. `int x^(3)e^(x^(2))dx=...` a) `(1)/(2)e^(x)(x^(2)-1)+c,` b) `(1)/(2)e^(x)(x^(2)+1)+c` c) `e^(x^(2))(x^(2)-1)+c,` d) `e^(x^(2))(x^(2)+1)+c`

If y=log((x^(2))/(e^(2))) then (d^(2)y)/(dx^(2)) equal to: a) -(1)/(x) b) -(1)/(x^(2)) c) (2)/(x^(2)) d) -(2)/(x^(2))

int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx is equal to (a) -x e^(x^(2)-(1)/(x))+c (b) x e^(x^(2)-(1)/(x))+c (c) (2x-1) e^(x^(2)-(1)/(x))+c (d) (2x+1) e^(x^(2)-(1)/(x))+c

int_(0)^(1)e^(2x)e^(e^(x) dx =)

d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b) 1 (c) (x^2+1)/(x^2-4) (d) e^x(x^2-1)/(x^2-4)

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

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

If int x e^(kx^(2)) dx = ( 1)/( 4) e^(2x^(2)) + C , then the value of k is

int2/((e^x+e^(-x))^2)\ dx (a) ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x))+C (c) (-1)/((e^x+1)^2)+C (d) 1/(e^x-e^(-x))+C

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

int ((1-x)/(1+x^(2)))^(2) e^(x)dx