# How do you find the integral of #sec(3x)sec(3x)#?

Considering that

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To find the integral of sec(3x)sec(3x), you can use the trigonometric identity: sec(x) = 1/cos(x). Rewrite sec(3x) as (1/cos(3x))^2. Then integrate using substitution or other appropriate techniques. Let u = 3x and du = 3dx. Rewrite the integral in terms of u. The integral becomes (1/9)∫du/(cos(u))^2. Use the trigonometric identity for secant squared to rewrite the integral. The integral becomes (1/9)∫du/(1 + tan(u)^2). The integral of (1 + tan(u)^2) is tan(u) + C, where C is the constant of integration. Therefore, the integral of sec(3x)sec(3x) is (1/9)tan(3x) + C.

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