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Advanced Placement (AP)
Owen Hunter
14 May, 10:33
Integrate sec (4x) tan (4x) dx
+3
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)
Jazlene Espinoza
14 May, 10:59
0
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
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