Question

integrate the function sec²(7 - 3x).dx

Answer 1

you can see your answer

Answer 2

I = ∫sec²(7- 3x)dx
Let t = 7 - 3x
differentiate both sides,
dt = 0 - 3dx
dt = -3dx
dx = -dt/3

hence, ∫sec²(7 - 3x)dx = ∫sec²t.(-dt/3)
= -1/3 ∫sec²t.dt
= -1/3 tant + C
now, put t = (7 - 3x)
= -1/3 tan(7 - 3x) + C

hence, answer, ∫sec²(7 - 3x)dx = -1/3tan(7 -3x) + C