What is the integral of 6sin(2x)+sec^2(x) ?

The integral of 6sin(2x)+sec^2(x) is -3cos(2x)+tan(x)+C

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integral of 6sin(2x)+sec^2(x)

\int 6 sin (2 x) + sec^{2} (x) d x

- 3 cos (2 x) + tan (x) + C

Solution steps

\int 6 sin (2 x) + sec^{2} (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 6 sin (2 x) d x + \int sec^{2} (x) d x

\int 6 sin (2 x) d x = - 3 cos (2 x)

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

= - 3 cos (2 x) + tan (x)

Add a constant to the solution

= - 3 cos (2 x) + tan (x) + C

What is the integral of 6sin(2x)+sec^2(x) ?
The integral of 6sin(2x)+sec^2(x) is -3cos(2x)+tan(x)+C