What is the integral of (3sec^2(4x)+3csc^2(4x)) ?

The integral of (3sec^2(4x)+3csc^2(4x)) is 3/4 tan(4x)-3/4 cot(4x)+C

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integral of (3sec^2(4x)+3csc^2(4x))

\int (3 sec^{2} (4 x) + 3 csc^{2} (4 x)) d x

\frac{3}{4} tan (4 x) - \frac{3}{4} cot (4 x) + C

Solution steps

\int 3 sec^{2} (4 x) + 3 csc^{2} (4 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 sec^{2} (4 x) d x + \int 3 csc^{2} (4 x) d x

\int 3 sec^{2} (4 x) d x = \frac{3}{4} tan (4 x)

\int 3 csc^{2} (4 x) d x = - \frac{3}{4} cot (4 x)

= \frac{3}{4} tan (4 x) - \frac{3}{4} cot (4 x)

Add a constant to the solution

= \frac{3}{4} tan (4 x) - \frac{3}{4} cot (4 x) + C

What is the integral of (3sec^2(4x)+3csc^2(4x)) ?
The integral of (3sec^2(4x)+3csc^2(4x)) is 3/4 tan(4x)-3/4 cot(4x)+C