Prove that `int_0^x e^(x t)e^-t^2dt=e^(x^(2)/4)int_0^x e^-(t^(2)/4)dt`

Prove that int_(0)^(x)e^(xt)e^(-t^(2))dt=e^(x^(2)//4)int_(0)^(x)e^(-t^(2)//4)dt .

Prove that int_(0)^(x)e^(xt).e^(-t^(2))dt=e^(x^(2)//4)int_(0)^(x)e^(-t^(2)//4)dt .

lim_(xrarroo)((int_(0)^(x)e^(t^(2))dt)^(2))/(int_(0)^(x)e^(2t^(2))dt) is equal to

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

lim_(x rarr0)(x^(e^(2^(2))))/(int_(0)^(x)e^(t^(2))backslash dt)=

lim_(x to oo)(int_0^(2x) te^(t^(2))dt)/(e^(4x^(2))) equals

int_e^(e(-1)) 1/(t(t+1)) dt

Find the derivative (dy)/(dx) of the following implicit functions : (a) int_(0)^(y) e^(-t^(2)) dt + int_(0)^(x^(3)) sin ^(2) t dt = 0 (b) int_(0)^(y) e^(t) dt + int _(0)^(x) sin t dt = 0 (c) int _(pi//2)^(x) sqrt(3 - 2 sin^(2)z ) dz + int_(0)^(y) cos t dt = 0

int(2e^(t))/(e^(3t)-6e^(2t)+11e^(t)-6)dt

If int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2))sin^(2)tdt=0 , then (dy)/(dx) at x=y=1 is