What is the integral of (2sec^2(x)) ?

The integral of (2sec^2(x)) is 2tan(x)+C

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integral of (2sec^2(x))

\int (2 sec^{2} (x)) d x

2 tan (x) + C

Solution steps

\int 2 sec^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= 2 tan (x)

Add a constant to the solution

= 2 tan (x) + C