Question

ʃ [e^(t-1/2)x] / t-1/2 dx

Answer 1

ignore the other variables besides the one that you are integrating with respect to\[\int\frac{e^{t-\frac12}x}{t-\frac12}dx=\frac12\frac{e^{t-\frac12}x^2}{t-\frac12}+C\]but if you didn't mean to mix x and t then you need to retype it

Answer 2

...unless t is a function of x or vice versa
but you didn't say that