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14 May, 10:33

Integrate sec (4x) tan (4x) dx

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  1. 14 May, 10:59
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    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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