# integral confusion

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
u=3x-2
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.

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1. 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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bobpursley

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