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
<span>All of us are a product of the culture we are raised in, the rules and regulations that we must follow and the spoken and unspoken world views that are passed on. We see the world from our perspective and our reality, we cannot help it, it is the filter we look at life through. Sometimes without even knowing how prejudiced we are, we form our opinions from the experiences we have had and what we have watched as we were growing up. Everything comes from a place deep within us that helps us make sense of the world and the people in it.</span>
Have you ever done community service or helped lead a big project? Even just some nice things you've done for your school.
