Answer:
sec(4x) + C
Explanation:
original problem: ∫sec(4x)tan(x)dx
use integration by substitution (u-sub) by setting u = 4x
if u = 4x, then du/dx = 4 and du = 4dx (dx = du/4)
after substitution the integral is ∫sec(u)tan(u)(du/4)
move the 1/4 out of the integral by using the integral Constant rule to form 1/4∫sec(u)tan(u)du
the anti-derivative of sec(u)tan(u) is sec(u), memorize your trigonometric derivatives!!!!
after integration, we get sec(u)/4 + C , now plug u back into the equation
sec(4x) + C is the general solution
You should first consult with past teachers of a similar subject to determine if they they think it's fitting and then to your counselor/ scheduling official. (Please be sure you have any prerequisites for the course, have summerwork/ projects to complete)
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Answer:
that's the line, just copy it
