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integral confusion

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integral of Sec[2x]Tan[2x]

i know u is sec 2x
du=2sec2xtan2x dx
what would i have to multiply with du so it would equal tan 2x dx?

if my question is confusing, then here's another example of what i'm talking about:
integral of (3x-2)^30 dx
du=3 dx
1/3 du=dx (i need help with this step on the problem obove)
then i would substitute and solve the integral.

  • integral confusion - ,

    Well, dx= du/(2sec2x tan 2x) from your equation.

    INT 2sec2x tan2x * dx= INT du
    INT du= u

    On the second.
    You have u^30 du/3 since dx=du/3
    INT u^30 du/3 = 1/3 INT u^30 du=
    1/3 * 31 u^31

    then on both, substitute back in the f(x) for u.

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