Relation on $\int_1^x\exp{t^2}dt$ Could you give me some leads to show the following relation :
$$\forall x>0, \int_1^x\exp{t^2}dt = \frac{1}{2x}\exp{x^2} + \frac{1}{4x^3}\exp{x^2} - \frac{3}{4}\mathbb{e}+ \frac{3}{4} \int_1^x \frac{1}{t^4}\exp{t^2}dt $$
Thanks in advance. 

Hint 1: multiply the integrand by $1 = \frac{t}{t}$, then use parts.
Hint 2: in parts, let $dv = t e^{t^2}dt$ always; an antiderivative is $\frac{1}{2} e^{t^2}$.
Hint 3: do this twice.
