How do you do this problem?

Step-by-step explanation:

∫ t⁷ e^(-t⁴) dt

If x = -t⁴, then dx = -4t³ dt, and ¼ x dx = t⁷ dt.

∫ ¼ x eˣ dx

If u = ¼ x, then du = ¼ dx.

If dv = eˣ dx, then v = eˣ.

∫ u dv = uv − ∫ v du

= ¼ x eˣ − ∫ ¼ eˣ dx

= ¼ x eˣ − ¼ eˣ + C

= ¼ eˣ (x − 1) + C

Substitute back:

= ¼ e^(-t⁴) (-t⁴ − 1) + C

find the vertical and horizontal asymptotes of the function f x = 5 x − 1 . to find the vertical asymptote, equate the denominator to zero and solve for . since the degree of the polynomial in the numerator is less than that of the denominator, the horizontal asymptote is .

step-by-step explanation: